Remainder of large numbers in c. How the Remainder Works .

Remainder of large numbers in c. Jul 23, 2025 · Algorithms for Large Numbers Large numbers, often exceeding the capacity of our everyday counting systems, require specialized algorithms for efficient manipulation. To find the GCD of two numbers in C, i. Note that 1017is quite a large number, but we found the remainders quite effortlessly! We quote the limerick by Martin Gardner about the modulus 10: There was a young fellow named Ben Who could only count modulo ten. Aug 1, 2025 · Divide two numbers, a dividend and a divisor, and find the answer as a quotient with a remainder. Bookmark the permalink. Let’s take some examples to see the remainders when divided by 11: 345: (5 + 3) – 4 = 2; 2 is the remainder. Perfect for arithmetic practice, financial calculations, and programming scenarios, it provides instant results for division operations while helping users Jul 23, 2025 · The GCD of two numbers is the largest positive integer that completely divides both numbers without leaving a remainder. What is the Remainder of 9602 Divided by 3? The remainder is 2, for 9602 ÷ 3. Why does C++ not have a built in way to express very large numbers? I wanted to write a program to compute 500th Fibonacci number and I needed an integer vector to do so. In mathematics, the greatest common divisor (GCD) of two or more numbers is the largest number that divides all the numbers in the set without leaving a remainder. The above example also showed us how to Normal types in C can usually only store up to 64 bits, so you'll have to store big numbers in an array, for example, and write mathematical operations yourself. When the remainder becomes 0, the last non-zero divisor is the GCD. Jul 5, 2025 · In this article we show how use the BigInteger type in C# to handle extremely large integer values that exceed the limits of built-in data types. Aug 9, 2011 · Which is the best way to find out whether the division of two numbers will return a remainder? Let us take for example, I have an array with values {3,5,7,8,9,17,19}. It rounds the quotient to the nearest integer (with halfway cases rounded toward the even number) and returns the difference between the numerator and the product of the rounded quotient and the denominator. I want to break it up into single-digit integers. Edit: To further improve your algorithm you can iterate through odd numbers only (after checking if you number is even) or, even How to Find the Remainder Whether you’re performing a standard division operation or performing long division, dividing one number by another involves calculating two quantities: the quotient and the remainder. It is part of the math library <math. How can I do this, especially if I don't know how many digits the integer In Java, computing the remainder of very large numbers can be effectively handled using the `BigInteger` class, which provides high-precision calculations beyond the limits of primitive data types. Oct 5, 2015 · The GMP library is usually a good reference for good algorithms. Sep 19, 2022 · List of C Programs List of All Programs Write C code to find quotient and remainder of the given number //Write a program to find the quotient and remainder of the numbers #include<stdio. The remainder() function returns the floating point remainder of the division dividend / divisor where the result of the division is rounded to the nearest integer (if the decimal part is exactly 0. Thus, modulus is 6 and quotient is 01371. 5 rounds to the nearest even integer. I want to code it in c++. The -1. Actual problem is that the number is quite large, around 10^100. While the result is the quotient, it is the sum of the two numbers. This process uses the referential congruence theorem in efficient division operations. Sep 30, 2023 · To find the remainder of large numbers using the congruence theorem, you leverage the concept of modular arithmetic. Division worksheets including division facts and long division with and without remainders. The Euclidean algorithm calculates the greatest common divisor (GCD) of two natural numbers a and b. it's getting rounded to zero. About Remainder Calculator Remainder Calculator is a useful online tool that assists users in doing division calculations. Jul 23, 2025 · In most programming competitions, we are required to answer the result in 10^9+7 modulo. Jul 21, 2018 · Remainder Theorem of Numbers | Remainder Problems in Aptitude Before going to concepts of remainder theorem of numbers, it is better to understand the the concepts of Divisor, Dividend, Quotient and Remainder Remainder Theorem Rule – 1 (Fundamental) Remainder of the expression can be expressed as positive remainders and negative remainders. if numerator is less than denominator then finish shift denominator as far left as possible while it is still smaller than numerator set bit in quotient for amount shifted subtract shifted denominator from numerator repeat the numerator is now the remainder The shifting need not be literal. See The GNU C Library in The GNU C Library Reference Manual. I have figured out the algorithm to sol Jul 23, 2025 · Given an integer a, b, m. say I have number of seconds and want to split that into minutes and seconds), what i Oct 3, 2013 · I would like to ask some help concerning the following problem. Program to find remainder when large number is divided by r in C++ Try this Program to find remainder when large number is divided by r in C++ (Version GNU GCC v11. Output is expected as an integer. . Remainder: The leftover portion after division. g. We know that by Fermat's theorem that since , then . But the remainder () function remains available, plus it works with real numbers and not just integers. Dec 23, 2024 · Write a program to find quotient and remainder of number in Java Script Write a program to find quotient and remainder of number in C# Explanation: In arithmetic, when dividing one number by another, we get two results: Quotient: The integer result of the division (ignoring the remainder). Table of contents The ring \ (\mathbb {Z}_n\) The Congruence Lemma 8. The inputs are scanned using the scanf () function and stored in the variables A and B. The primary research citation on the practical use of modular arithmetic for large numbers is [1]. Competitive programming problems often require solving such congruence relations. Examples: Input : sa = 2 Dec 3, 2024 · Here is the algorithm for finding power of a number. He said, “When I go Past my last little toe, I shall have to start over again. GCD is an important concept that plays a crucial role in various fields, including number theory, cryptography, computer science, and engineering. 3M subscribers Subscribed Apr 6, 2023 · Given a number N, the task is to find the remainder when N is divided by R (a two-digit Number). The dividend is the number being divided and is the first number in a division problem, written either above the division line or to the left of the division symbol (÷). Mar 13, 2010 · For large number arithmetic in C++, use the GMP library. Also I think that "big numbers" algorithms (storing a number as an array) will not work for me too (500*10^9) is too much operations. Solved Example on Chinese Remainder Theorem Suppose a certain number leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 2 when divided by 7. Use our free Remainder Calculator to quickly find quotients and remainders in division problems. There's this code :- int res = 0; //num contains the Jul 12, 2025 · In C or C++, the modulo operator (also known as the modulus operator), denoted by %, is an arithmetic operator. We will now apply these theorems to finding remainders of rather large numbers. Apr 10, 2020 · Getting the remainders of large numbers is actually an active field of research in the mathematics and computational industries. How the Remainder Works May 16, 2024 · Learn how to generate random numbers in C using the rand() function, set seed, work with ranges, and avoid repetitions. Finally, we append the sign to the quotient to get the final result. So if the actual answer is very large, with the use of modulo m m, it would be sufficient to use the data types int and long long. Therefore, dividing the factorial number by 5, recursively, and adding the quotients, you get the number of trailing zeros in the factorial result E. The remainder() function is defined in the <cmath> header file. The dividend becomes the remainder, and the number of times subtraction is done becomes the quotient. There exists an approach that works for large numbers also. In contrast to fmod (), the returned value is not guaranteed to have the same sign as x. Sep 19, 2024 · Now, convert both the dividend and divisor to positive numbers and keep subtracting the divisor from the dividend until the dividend becomes less than the divisor. Get step-by-step guidance and examples. But division takes a very long time, how it cou Nov 11, 2024 · Returns Remainder: The result of a % b is the remainder after dividing a by b. Apr 29, 2024 · Given a large number (represented as a string) which has to divide by another number (represented as int data type). Jan 13, 2015 · Okay, so you want to calculate $a^b\ mod \ m$ with $b$ and m are very large numbers and a and m are coprime. Sep 27, 2020 · Suppose I have a large number (around 10^5 digits) and I have to calculate num % a where a is less than 10^9 i. The libraries I saw utilized a typedef struct to store each intal. [Algorithm 18_001] Lucas theorem and the remainder of large combination numbers, Programmer Sought, the best programmer technical posts sharing site. Subtract and divide the numbers until you find a difference that yields an integer when divided by the smaller number, which will be the remainder. This essential math tool simplifies complex calculations for students, teachers, and professionals. The absolute maximum primitive data type in C++ is unsigned long long int with a maximum Jul 23, 2025 · This theorem is used to find the remainder of a number raised to a large power modulo n efficiently. The question said to print the remainder. Jul 15, 2025 · For calculating the remainder we first calculate the original value for number 7126 and divide it by 48 and obtain the remainder. And if all we want is the remainder modulo \ (n\) of a series of additions, multiplications, subtractions applied to some numbers, we can take remainders at every step so that the Modulo Operation The modulo (or "modulus" or "mod") is the remainder after dividing one number by another. Is Apr 24, 2020 · At some point you can make numbers large enough that computers have a hard time takings modulo on them. GeeksforGeeks | A computer science portal for geeks Mar 11, 2019 · However, I'm trying to test whether the very large integer number is divisible without remainder by another number. Apr 10, 2023 · Given a big number 'num' represented as string and an integer x, find value of "num % a" or "num mod a". The large number can be very large which does not even fit in long long in C++. Create an array res [] of MAX size and store x in res [] array and initialize res_size as the number of digits in x. Feb 1, 2010 · How to calculate modulus of 5^55 modulus 221 without much use of calculator? I guess there are some simple principles in number theory in cryptography to calculate such things. Learn the efficient methods to calculate the remainder of very large numbers using the C programming language. Note: This function is the same as fmod () except that fmod() truncates the result of the division instead of rounding it. For ex Overview When the answer to a problem is a very large number, problem setters expect you to output it "modulo m m ", that is, the remainder after dividing the answer by m m (for example, "modulo 1 e 9 + 7 1e9+7 "). Mar 19, 2020 · Therefore having $7^ {12345678}$ % $5$. The number by which you divide the dividend is indicated as the divisor. I tried finding the length of modulo periods, but they are mush longer, than 10, and even unsigned long long int can't deal with such big numbers (239^10). We can use this technique to find quotient and remainder of big numbers also. Jul 23, 2025 · In C/C++ the number of digits a long long int can have is a maximum of 20. ” Problems: 1. Examples: Input: a = 426, b = 964, m = 235 Output: 119 Explanation: (426 * 964) % 235 = 410664 % 235 = 119 Input: a = 10123465234878998, b = 65746311545646431 m = 10005412336548794 Output Oct 6, 2014 · I wrote a program to divide large numbers using strings in C++. Finding Remainder | Binomial Theorem | Crack In Seconds | Unacademy JEE | JEE Maths | Nishant Sir Unacademy JEE 2. This tutorial covers the basics of working with BigInteger in C# for developers who need high-precision number calculations. (since C++23) Nov 20, 2019 · Given a sting of a big number say num and another big number say m; the task is to print the quotient using divide operation and the remainder of the big number using modulus. Examples : Input : num = 1234 Output : 2 Input : num = 1232 Output : 0 Input : num = 12345 Output : 4 Simple Approach is to convert a string into number and perform the mod operation. Modulus of Positive Numbers Problem: What is 7 mod 5? Solution: From Quotient Remainder Theorem, Dividend=Divisor*Quotient + Remainder 7 = 5*1 + 2, which gives 2 as the remainder. The long division can be used to find the remaining division problem quickly. Jun 19, 2009 · I have a big number (integer, unsigned) stored in 2 variables (as you can see, the high and low part of number): unsigned long long int high; unsigned long long int low; I know how to add or subtr Feb 6, 2023 · This function is also used to return the remainder (modulus) of 2 floating point numbers mentioned in its arguments. How to Use the Modulo Operator Using the modulo operator is straightforward. Perfect for students, teachers, and anyone needing fast, accurate division results. Oct 23, 2024 · Master mathematical operations in C with our comprehensive guide. Find the remainder of dividing $6^{83}+ 8^{83}$ by $49$ Are there any theorems/rules to compute the answer ? Jul 23, 2025 · The modulus operator, denoted as %, returns the remainder when one number (the dividend) is divided by another number (the divisor). I had a look at similar formats like How would I find the modulo of a large number without using a calculator that supports large numbers?, but I haven't learned any of the following rules/theorems. The reason behind this is, if problem constraints are large integers, only efficient algorithms can solve them in an allowed limited time. e. Examples: Input: N = 13589234356546756, R = 13 Output: 11 Input: N = 3435346456547566345436457867978, R = 17 Output: 13 Get the digit of N one by one from left to right. May 25, 2018 · I Have a large string (around 1000 characters) , which is binary. Jul 12, 2025 · This method is often used for calculations modulo non-prime number M; in this case a number is stored as powers of divisors of M which divide the number, plus the remainder modulo M. Factorial of a number Examples: Input: 100 Output Mar 25, 2015 · The problem is that I want to overload operator %, so than I can get the remainder of two large numbers. 123 would turn into 1, 2, and 3. I am unsure of how I should do the rest to find the final remainder. Let's now rewrite the exponent 345 = 34 (10) + 5. Jul 8, 2013 · "The Modulus is the remainder of the euclidean division": According to the Wikipedia article you've referenced, the modulus is the divisor in the modulo operation, not the remainder: "the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, the latter being called the modulus of the operation. And the question is to store the 22 digit number which is not easy to store in any kind of primitive type. The quotient computed is rounded. This algorithm Enter divisor: 4 Quotient = 3 Remainder = 1 The division operator / computes the quotient (either between float or integer variables). Then divide the three-digit number by 8 and find the remainder using long division. So to deal with this type of problem let's design a new data type which is going to be called BigInt In this article, a few basic operations are being implemented on the new data type. Below are the steps Long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It returns the remainder of dividing the first operand by the second operand. Apr 9, 2025 · What is a Calculator with Remainder? A calculator with remainder helps solve division problems showing both quotient and remaining value. Now i need to divide it by the given number as converting the binary string to decimal itself becomes too large to represent. But you shouldn't reinvent the wheel here - you could try the GNU Multiple Precision Arithmetic Library for this purpose. This online Editor and Compiler provide you the comfort to edit and compiple your source C++ code using latest version GNU GCC v11. Oct 16, 2020 · The biggest problem is you are returning long long (a 64-bit value) from a float -- a 32-bit value on x86 and x86_64. (This is of course equivalent to modulo of the divisor, mathematically. There's a neat little way to do this using exponents. Technically both positive and negative remainders To find the remainder when dividing a number by 8, first form a three-digit number from the last three digits of the integer. Let's say I have an integer called 'score', that looks like this: int score = 1529587; Now what I want to do is get each digit 1, 5, 2, 9, 5, 8, 7 from the score using bitwise operators(See below how do i find the remainder of 10^400 divided by 17? Thanks!$-If you raise 10 to a set of powers, it will cycle through a repeating set of values modulo 17. 6. The operator for doing modulus operation is I am just wondering, if I want to divide a by b, and am interested both in the result c and the remainder (e. Jul 23, 2025 · Factorial of a non-negative integer, is the multiplication of all integers smaller than or equal to n. In particular, a boolean variable can be included in each intal to specify whether it represents a positive or negative number. I used continuous subtraction to get the remainder and quotient. Using this, we can technically store the number large enough to ever need more size. Their documented algorithms for division mainly depend on choosing a very large base, so that you're dividing a 4 digit number by a 2 digit number, and then proceed via long division. For exponentiation, you will have to use The return value for two numbers a and b is approximately equal to a - round(a/b) * b except that a decimal part of exactly 0. These algorithms are crucial in various fields, including cryptography, scientific computing, and financial modeling. Negative Numbers: The behavior of the modulo operator can be different with negative numbers, which is worth noting. It is theorised that a perfect algorithm for solving remainders in a feasible amount of time when the numbers are mathematically large is impossible and forms the backbone for a lot of encryption techniques. The quotient is the result of dividing a number (dividend) by another number (divisor). As you can see, the first number is about 3 billion symbols. 3. Khan Academy Khan Academy This method asks you to perform successive division, first of the smaller of the two numbers into the larger, followed by the resulting remainder divided into the divisor of each division until the remainder is equal to zero. C/C++. This question was asked in a competitive exam. The modulo division operator produces the remainder of an integer division which is also called the modulus of the operation. Jun 12, 2024 · Working with Big Numbers in C To handle large numbers in C, we can use arrays or strings to store individual digits of the large number and perform operations on these digits as required. What is modulo operation: The remainder obtained after the division operation on two operands is known as modulo operation. Hence it follows that: (1) Jul 26, 2024 · The remainder when a number is divided by 11 = (difference of the sum of the digits in the odd position and the sum of the digits in the even position) modulo 11. For example if N is divisible by 3 then you'll need 2 iterations to find the answer - in your case it would be about N/6 iterations. However, they are smaller than half of the maximum allowed long long int value. If the returned value is 0 , it will have the same sign as x. When |n-x/y| = ½, the value n is chosen to be even. h> in C and <cmath> in C++. Apr 26, 2025 · In C, the division operation might not work the same way as in regular arithmetic if you’re working with integers. fmod () in C The fmod () function returns the remainder of the division of two floating-point numbers. Mar 9, 2013 · I am stuck with a problem where I need to find remainder of a very large number using a prime number. For example I have a factorial program that needs to save really huge integers that can be 50+ digits long. This would eliminate the limitation of only being able to handle positive numbers. i. Sep 25, 2023 · We can now state the remainder rule for 11: the remainder when a number is divided by 11 is the difference of the sum of the digits in the odd position starting from the right and the sum of the digits in the even position. Multiply (res [], x) 1. I was searching the Internet for the fastest way to calculate thi Use the free online calculator to find the remainder from the division of two numbers, contains useful definitions, methods to find remainder, solved examples & FAQs. This tool is indispensable for researchers, mathematicians, and professionals who regularly work with extraordinarily large or small numbers in fields like cryptography, statistical analysis, and computational sciences. We will solve this problem by breaking it down. ---Efficiently Calculate the Remainder of Very I need some help with this problem: $$439^{233} \\mod 713$$ I can't calculate $439^{223}$ since it's a very big number, there must be a way to do this. Jan 7, 2014 · This allows you to multiply two signed numbers a and z both with a certain modulus m without generating an intermediate number greater than that. 00 result makes sense given the parameters of the remainder () function. 5 it rounds to the nearest even integer). This concise guide will clarify this essential operator for your coding journey. Jul 7, 2024 · The fmod () function in C computes the floating-point remainder of the division of two numbers. Overloading operator *, - between large numbers is finished by dealing with every digit of the large number. I'm creating a computer application in which I need to be able to calculate the remainder of large numbers (more then $30$ digits). This calculator can be This article explains how to calculate the remainder of a large number when divided by r in C++. Also Read: C++ remainder () C++ div () C++ Operators Share on: Dec 13, 2018 · Functions to handle big numbers in C Ask Question Asked 6 years, 7 months ago Modified 6 years, 5 months ago Sep 28, 2015 · Find the remainder of a number with a large exponent [duplicate] Ask Question Asked 9 years, 11 months ago Modified 7 years, 1 month ago Mar 12, 2025 · This article introduces the modulo operator in C, explaining its usage and applications. Introduction In the realm of C programming, managing large integer operations presents significant challenges due to inherent size limitations of standard integer types. It is designed to return the outcome of any division operation specifically by giving both the quotient and the remainder. We can use an interesting result called Euler's theorem: $$ a^ {\phi (m)} \ mod \ m=1$$ Long division is the method for dividing a large number (dividend) by a smaller number (divisor) to get a quotient and remainder. In this C programming example, you will learn to find the quotient and remainder when an integer is divided by another integer. The library provides overloads of std::remainder for all cv-unqualified floating-point types as the type of the parameters. The HCF of two numbers can be calculated with the help of Euclid's division lemma by following these steps. Perfect for beginners and experienced programmers alike. How should i go about it? I tried doin Jan 18, 2015 · 6 I'm trying to write a C program which performs multiplication of two numbers without directly using the multiplication operator, and it should take into account numbers which are sufficiently large so that even the usual addition of these two numbers cannot be performed by direct addition. Find (a * b ) mod m, where a, b may be large and their direct multiplication may cause overflow. Works with Integers: The modulo operator only works with integers in C/C++. Jan 4, 2022 · The remainder refers to what is left after a long division process in mathematics. Learn arithmetic operators, order of operations, using parentheses, and practical examples for beginner C programmers. Check out the GNU MP library or Flint (Fast Library for Number Theory, take a peek at the (header only!) C++ precision package or take a peek at Wikipedia's list. 0. Examples: Input : number = 1260257 divisor = 37 Output : 34061 (See below diagram) Input : number = 12313413534672234 divisor = 754 Output Here's the method I used to solve the problem, this was achieved by reading the comments below: Solution -- The number 5 is a prime factor of any number ending in zero. Examples : Input: num = "12316767678678", a = 10 Output: num (mod a) ? 8 The idea is to process all digits one by one and use the property that xy (mod a) ? ( (x (mod a) * 10) + (y (mod a))) mod a where, x : left-most digit The easiest division algorithm to implement for large numbers is shift and subtract. The number is stored in a string whose maximum length is 1000. The greatest common divisor is Online Remainder Calculator performs Euclidean division of two integer numbers (positive or negative ) to find the quotient and remainder. , the largest number that exactly divides the numbers, you can use the Euclidean approach, loops, recursion, etc. " Sep 3, 2025 · Modular arithmetic is a system of arithmetic for numbers where numbers "wrap around" after reaching a certain value, called the modulus. Below is the implementation of above approach : a a a — Initial number you want to divide, called the dividend; n n n — Number you divide by; it is called the divisor; q q q — Result of division rounded down to the nearest integer; it is called the quotient; and r r r — Remainder of this mathematical operation. This process continues until the remainder is no longer divisible by the divisor. This function is useful for scenarios where the rounding of the quotient is critical. It yields the remainder resulting from the integer division of one number by another. That is a string is used to store each digit of the number. This allows some meta-data about each intal to be stored easily. Power (n) 1. Learn how to check even and odd numbers, use it in loops, and see clear examples to enhance your programming skills. I still prefer the div () function to obtain a more realistic answer. And as the comments already pointed out, the ^ operation is binary XOR. But this approach will not work for long strings. It is particularly useful when dealing with periodic functions, angles, or any scenario where the remainder after division is Jan 27, 2020 · If you really need very large integers (like in many cryptographic applications), there are several open source libraries around. The task is to find the division of these numbers. Observe the following long division method to see how to divide step by step and check the divisor, the dividend, the quotient, and the remainder. How do you Write a Remainder as a Fraction? Feb 3, 2018 · Say I have a multi-digit integer in C. You could do this the long way - calculate Explanation This GCD program in C uses Euclid’s algorithm, which iteratively calculates the remainder of the division between two numbers. Add two big integers Nov 13, 2013 · How to find remainders of large numbers using negative remainders How to calculate remainders of a number with power using the Fermat’s and Euler’s theorem. 2. In mathematics, a remainder is the residual amount left after division when one number cannot be accurately divided by another. Mar 5, 2025 · Unlock the magic of numbers as you learn how to use modulo in C++. Using Division and Modulo Operator In the below program, to find the quotient and remainder of the two numbers, the user is first asked to enter two numbers. It is a very long and time-consuming process and it is not at all feasible to solve it in this way. I need to create a function that will multiply two integers and extract the remainder of this multiplication divided by a certain num May 23, 2024 · The IEEE floating-point remainder of the division operation x/y calculated by this function is exactly the value x - n * y, where the value n is the integral value nearest the exact value x/y. Jul 14, 2025 · We initialize the result as 1 and iterate from 1 to n, updating the result by multiplying it with x and taking the modulo by M in each step to keep the number within integer bounds. Let's take two numbers 'c' and 'd' for which we need to find the HCF such that c > d. Thanks. This entry was posted in Lesson by dgookin. It's based on an approximate factorisation of the modulus m, remainder = numer - rquot * denom Where rquot is the result of: numer / denom, rounded toward the nearest integral value (with halfway cases rounded toward the even number). it is in the int range of C++. For example, you Apr 23, 2022 · 5) quo[5] = (1 * 10 + 5) / 9 = 15 / 9 = 1 mod = (1 * 10 + 5) % 9 = 15 % 9 = 6 Concatenating all values of quotient together (from 1 to n) where n is the number of digits. In particular, the mpz_mod function would do this. remainder = number - rquot * denom Where rquot is the result of: number/denom, rounded toward the nearest integral value (with halfway cases rounded toward the even number). This article will delve deep into the nuances of division in C, focusing on quotient and remainder There are functions in the standard C library to calculate remainders from integral-values division of floating-point numbers. The modulus operator % computes the remainder when one integer is divided by another (modulus operator cannot be used for floating-type variables). Mar 26, 2024 · The modulus operator, often represented by the symbol '%', is a fundamental arithmetic operator used in programming languages to find the remainder of a division operation between two numbers. ) Jun 24, 2024 · The Big Number Calculator facilitates complex arithmetic operations with large numbers that standard calculators cannot handle efficiently. Nov 18, 2016 · The internet is full of algorithms to calculate the modulo operation of large numbers that have the form $a^e \\bmod p$. h> int main() Apr 1, 2019 · Please watch this video to find the remainder of a number with large power or complex numerical expressions when divided by natural numbers. First note that 2 is not divisible by 11. Long division will require computing 2 digit by 1 digit quotients; this can either be done recursively, or by precomputing an inverse and Jul 11, 2025 · Given two numbers sa and sb represented as strings, find a b % MOD where MOD is 1e9 + 7. It mainly uses remainders to get the value after wrapping around. The input of the Number may be very large. Why not simply use a union between float and unsigned to get the unsigned representation of the float? That would make it easy to output the binary representation. The divisor The Remainder Operator (%) What is the Remainder Operator? In C++, the modulus operator is represented by the symbol %. G. BigInteger represents an arbitrarily large signed integer. Example 1 Calculate the least residue of . Do following for all numbers from i=2 to n . This approach is efficient and widely used for large numbers, as it avoids checking all divisors. Learn how to solve long division with remainders, or practice your own long division problems and use this calculator to check your answers. Syntax : Jul 23, 2025 · Here, we will see how to find the quotient and remainder using a C++ program. Long division with remainders is one of two methods of doing long division by hand. For a more natural C++ wrapper, the mpz_class class can help by providing operator overloading for multiprecision operations. Jul 23, 2025 · In Knuth’s Modular Multiplication, CRT speeds up large-integer multiplication in cryptographic libraries. Jul 23, 2025 · Given a large number as a string, find the remainder of number when divided by 7. The method is extensively discussed by Knuth inhissecondvolume[6]; thatbookismyprimarysourcefortheChineseremaindertheorem and its proof. - Number of trailing zeros in 126! = 31 126/5 = 25 remainder 1 25/5 = 5 Jul 11, 2025 · Output: Quotient = 0, Remainder = 2 Input: A = 17, B = 5 Output: Quotient = 3, Remainder = 2 1. 1 says that two numbers are congruent iff their remainders are equal, so we can understand congruences by working out arithmetic with remainders. The dividend is the number to divide. It is the most common method used to solve problems based on division. I have already made a function of multiplication of long numbers, addition of long numbers, subtraction of long numbers and division of long numbers. The greatest common divisor g is the largest natural number that divides both a and b without leaving a remainder. Aug 23, 2010 · First thought you can find the smallest divisor d (not equal to 1 of course), then N/d will be the largest divisor you're looking for. For large number arithmetic in C++, use the GMP library. We use Euclid's division lemma to find the HCF of large numbers which is typically difficult to calculate using basic HCF calculation techniques. Thus, to find 7 mod 5, find the largest number that is less than or equal to 7 and Apr 7, 2018 · I am solving a programming problem where I have to print the answer in the format answer mod 10 ^ 9 + 7, where 'answer' is the actual answer to the problem. One prominent algorithm for handling large numbers is the Karatsuba multiplication algorithm . Get the modulo of a very large number that cannot be stored in any data type in C/C++! Jul 23, 2025 · Methods to Handle Large Numbers in C++ One of the most prominent method that is used to handle large numbers is the use of array and strings to store the digits of the number. This tutorial delves into practical techniques and strategies for effectively handling computations that exceed traditional integer boundaries, providing developers with essential skills to overcome numeric constraints in Jul 6, 2017 · I'm trying to get the remainder of a large number, for example: 1551690021432628813 % 64 But I find that the it's a couple of digits too long for JavaScript. The numbers a and b can contain upto 10 6 digits. Multiply x with res [] and update res [] and res_size to store the multiplication result. 0) to Edit, Run, and Share your C++ Code online directly from your browser. How about numbers with unknown factorization GeeksforGeeks | A computer science portal for geeks Dec 9, 2019 · How do I calculate the remainder of $30^{29} \\pmod {51}$? I cant use Fermat's little theorem since $51$ is not a prime number. Feb 9, 2025 · 1-3) Computes the IEEE remainder of the floating point division operation x / y. Synonyms for GCD include greatest common factor (GCF), highest common factor (HCF), highest common divisor (HCD), and greatest common measure (GCM). In this article, we will learn to calculate the GCD of two numbers in the C programming language. Aug 1, 2019 · I have a question, which is to find the modulo 11 of a large number. We would like to show you a description here but the site won’t allow us. When used in a C++ expression, the syntax is straightforward: int result = a % b; Here, the value of `result` will contain the remainder when `a` is divided by `b`. kdymn cddd dbuk qacgiz icuxpn jnmzs mnciay igc joqouss sjruxsk