What is modulo?
Take two numbers and then divide the first number by the second number, then the rest is called the module.
Commonly called “Modulo Operator”, it's easier to solve module operation with our Modulo Calculator because all you have to do is enter the values in the calculator fields and press the Calculate button!
How to calculate modulo?
Let's be honest. Sometimes the best modulo calculator is the one easy way to find modulo. It doesn't even require us to know what the module formula is in the first place! But if you want to know the exact module calculation formula, please see the “Modulo Formula" below:
Modulo Formula: the remaining mod of a/b is the mod of two numbers a and b
Because two numbers, a (dividend) and n (divisor), a modulo n (abbreviated as mod n) is the remainder of a by n division. For example, the expression "7 mod 5" would be 2 because 7 divided by 5 leaves a remaining 2 while "10 mod 5" would be 0 because the 10 by 5 division leaves a remaining 0.
- Our modulo calculator can be used to determine the outcome between integer numbers of modulo operations.
- The modulo operation, which is also frequently referred to as the modulus operation, identifies the remainder after dividing a given number by another number.
- Modulo is often expressed as mod b, but can be expressed as a percent b in some cases.
- Modulo is often calculated on calculators using mod () function: mod(a, b) = r.
- In this representation, a is the dividend, mod is the operator of the modulus, b is the divisor, and r is the remainder after the divisor (b) divides the divided (a).
Applications of Modulo Calculator
- Modular arithmetic is one of the foundations of number theory in theoretical mathematics which touches almost all aspects of its study, and is also widely used in group theory, knot theory, ring theory and abstract algebra. It is used in applied mathematics in computer algebra, cryptography, computer science, chemistry, and visual and musical arts.
- A very practical application is to calculate checksum within serial number identifiers. For example, the International Standard Book Number (ISBN) uses arithmetic for error detection modulo 11 (if issued before 1 January 2007) or modulo 10 (if issued on or after 1 January 2007). Likewise, for example, International Bank Account Numbers (IBANs) use modulo 97 arithmetic to spot user input errors in bank account numbers. In chemistry, a check digit calculated by the last digit for the first two sections of the CAS registry is one (a unique identifying number for each chemical compound), the previous digit 2 is a check digit, and the previous digit 3 etc., the sum module 10 adds all these up and calculates.
- Modular arithmetic supports public key systems directly in cryptography such as RSA and Diffie–Hellman. It offers finite fields which support elliptical curves and is used in a variety of key symmetric algorithms including International Data Encryption Algorithm (IDEA), RC4, and Advanced Encryption Standard (AES). RSA and Diffie–Hellman use modular exponentiation.
- Modular arithmetic is commonly used in computer algebra to limit the size of integer coefficients in intermediate calculations and data. It is used in factorization of polynomials, a problem for which all known efficient algorithms use modular arithmetic. It is used by the most efficient implementations of the most common polynomial divisor, exact linear algebra and Gröbner based algorithms over the integers and rational numbers.
- Modular arithmetic is often used in computer science for bitwise operations and other operations involving cyclic fixed-width data structures. As implemented in many programming languages and calculators, the modulo operation is a modular arithmetic application which is often applied in this context. The XOR logical operator sums 2 bits, Modulo 2.
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