Modulo Calculator

About Modulo Calculator

The modulo operation returns the remainder after integer division. It is fundamental in number theory and programming.

How to use this calculator

1. Enter the dividend, the number you want to divide, as \(a\).
2. Enter the divisor, the number you are dividing by, as \(b\).
3. Click calculate to find the remainder \(r\).
4. Use the result to see how many are left over after equal groups are made.

The formula explained

The formula \(a \mod b = r\) computes the remainder \(r\) after dividing \(a\) by \(b\). If the division is exact, the remainder is 0.

• a = the dividend, the number being divided
• b = the divisor, the number dividing into the dividend
• r = the remainder left after division

Step by step method

1. Divide \(a\) by \(b\) and find the whole-number quotient.
2. Multiply the quotient by \(b\).
3. Subtract that product from \(a\) to get the remainder.

Worked example

Problem. Find \(47 \mod 5\).

1. Divide 47 by 5. The quotient is 9 because \(5 \times 9 = 45\).
2. Subtract 45 from 47, so \(47 - 45 = 2\).
3. The remainder is 2.

Tips and common mistakes

• The remainder is always smaller than the divisor when the divisor is positive.
• If a number divides evenly, the modulo result is 0. For example, \(24 \mod 6 = 0\).

Frequently asked questions