Modulo Calculator - Mod N % - Online Modulus Finder

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Tool to compute any modulo operation. Modulo is the name of the calculation of the remainder in the Euclidean division. The modulo calculator returns the rest of the integer division.

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Modulo N Calculator - dCode

Tag(s) : Arithmetics

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Modulo N Calculator

1. Mathematics
2. Arithmetics
3. Modulo N Calculator

Mod Calculator (A mod N)

Number A Integer N (Modulo %) Only return positive modulos Calculate a % n See also: Euclidean Division

Modular Exponentiation Calculator (a^b mod n)

⮞ Go to: Modular Exponentiation

Modular Equation Solver (Find x mod n)

⮞ Go to: Modular Equation Solver — Chinese Remainder

Modular Inverse Calculator (a^-1 mod n)

⮞ Go to: Modular Multiplicative Inverse

Answers to Questions (FAQ)

What is a modulo in math? (Definition)

The modulo is the name of a mathematical operation that, for 2 numbers $ a $ and $ b $, calculates the remainder $ r $ of the Euclidean division $ a \div b $. Mathematically the modular calculus is written $$ a \equiv r \mod{b} $$

Example: A heap of $ a = 123 $ marbles divides into $ b = 10 $ heaps of $ 12 $ marbles and there remain $ r = 3 $ marbles. So the modular calculation $ 123 $ modulo $ 10 $ is equal to $ 3 $, or $ 123 \equiv 3 \mod{10} $

The modulo operator is sometimes noted a%b=r with the percent sign %.

Modular calculations are often imaged with a circle, like on a clock where hour calculations are done modulo 12 (or 24) for hours and modulo 60 for minutes.

Example: It is 3:00 am, in 25 hours it will be 4:00 am, is equivalent to the calculation $ 3 + 25 \equiv 4 \mod{12} $ or even (3+25)%24=4 The minute hand is $ 15 $, in $ 90 $ minutes it will be $ 45 $, because $ 15 + 90 \equiv 45 \mod{60} $

How to calculate a Modulo A % N?

Method 1: Perform euclidean division and returns the remainder.

Example: Calculate $ A=123 $ modulo $ N=4 $, perform the Euclidean division of $ 123 / 4 = 30 \text{ r } 3 $ as $ 123 = 30 \times 4 + 3 $ (the quotient is $ 30 $, and the remainder is $ 3 $). The modulo is the value of the remainder, so $ 123 \equiv 3 \pmod{4} $.

The negative modulo can be considered (rare), in this case $ 123 = 31 \times 4 - 1 $, so $ 123 \equiv -1 \pmod{4} $.

dCode uses this method that applies to both large numbers, as point numbers for A. However, N be a natural number.

Method 2: Perform the integer division and calculate the value of the difference.

Example: Calculate $ A=123 $ modulo $ N=4 $, make the division: $ 123/4 = 30.75 $. Keep the integer part $ 30 $, and multiply by $ N=4 $, $ 30 \times 4 = 120 $. The difference between $ 123 $ and $ 120 $ is $ 3 $, so $ 123 \equiv 3 \pmod{4} $.

How to write a modulo?

A modulo (from latin modulus) calculation can be written differently:

In Mathematics, write it using the $ \equiv $ congruence symbol and the keyword mod :

$$ 123 \equiv 3 \mod 10 $$

For computer, write the % percentage symbol, easily accessible on a keyboard:

$$ 123 \% 10 = 3 $$

In functional programming, for integers there is often the function mod() and for floating point numbers, the function fmod().

On calculators, it is often implemented with the function mod():

$$ \mathrm{mod} (123,10) = 3 $$

In spreadsheets like Excel, use MOD(A1;A2)

How to calculate a^b mod n?

This calculus is named modular exponentiation. It consists of calculating the remainder of the division of $ a^b $ by $ n $, without directly calculating $ a^b $. dCode has a tool dedicated to modular exponentiation.

How to calculate a^-1 mod n?

This calculation is called a modular inverse. The modular inverse of $ a $ modulo $ n $ is the number $ x $ such that $ a imes x quiv 1 \mod n $. dCode has a tool dedicated to modular inverses.

Where is the modulo in operators' precedence order?

In most programming languages, the % (modulo) operator has the same precedence as multiplication and division, and is evaluated from left to right.

What is the difference between modulo and congruence?

Modulo is an operation (calculating the remainder).

Congruence is a relationship: $ a \equiv b \mod n $ means that $ a $ and $ b $ have the same remainder when divided by $ n $

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Summary

• Mod Calculator (A mod N)
• What is a modulo in math? (Definition)
• How to calculate a Modulo A % N?
• How to write a modulo?
• How to calculate a^b mod n?
• How to calculate a^-1 mod n?
• Where is the modulo in operators' precedence order?
• What is the difference between modulo and congruence?

Similar pages

• Euclidean Division
• Modular Exponentiation
• Chinese Remainder
• Modular Equation Solver
• Modular Multiplicative Inverse
• Modulo Cipher
• Fill The Blanks Equation Solver
• DCODE'S TOOLS LIST

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