Enter a mod b statement(s)

Perform the modular arithmetic
7mod3+5mod8-32mod5

Determine 7 mod 3

Define modulus:

Remainder of a ÷ b
In this case, a = 7 and b = 3

Calculate whole number part:

3 goes into 7 a total of 2 times
3 x 2 = 6

Calculate remainder part:

Remainder = a - whole number
Remainder = 7 - 6

Excel or Google Sheets formula:

=MOD(7,3)

Determine 5 mod 8

Define modulus:

Remainder of a ÷ b
In this case, a = 5 and b = 8

Calculate whole number part:

8 goes into 5 a total of 0 times
8 x 0 = 0

Calculate remainder part:

Remainder = a - whole number
Remainder = 5 - 0

Excel or Google Sheets formula:

=MOD(5,8)

Determine -32 mod 5

Define modulus:

Remainder of a ÷ b
In this case, a = -32 and b = 5

Calculate whole number part:

5 goes into -32 a total of -7 times
5 x -7 = -35

Calculate remainder part:

Remainder = a - whole number
Remainder = -32 - -35

Excel or Google Sheets formula:

=MOD(-32,5)

Simplify our modular arithmetic:

1 + 5 + 3 = 9

What is the Answer?

-32 mod 5 ≡ 3

How does the Modulus Calculator work?

Free Modulus Calculator - Given 2 integers a and b, this modulo calculator determines a mod b or simplifies modular arithmetic such as 7 mod 3 + 5 mod 8 - 32 mod 5
This calculator has 1 input.

What 1 formula is used for the Modulus Calculator?

amodb = Remainder after a ÷ b

For more math formulas, check out our Formula Dossier

What 2 concepts are covered in the Modulus Calculator?

modulus: the remainder of a division, after one number is divided by another.
a mod b
remainder: The portion of a division operation leftover after dividing two integers

Example calculations for the Modulus Calculator

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