Power Calculators

🧮 Modular Arithmetic Calculator

Calculate the remainder of an integer after division by a positive modulus.

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Enter details

Remainder
3

Also available in our Android app, with charts and full breakdown tables.

📘 About the Modular Arithmetic

Use modular arithmetic to find expressions such as 123 mod 10.

The modulus must be non-zero.

🧮 Formula

Modulo operation
a mod m

Where

  • a = number
  • m = modulus
  • remainder = a - floor(a/m)m
For standard elementary use, enter positive integers.

✏️ Worked example

123 modulo 10

You enter
Number123
Modulus10
You get
Remainder3

The remainder is 3.

Try this example →

🧭 How to use this calculator

What you enter

  • Number
  • Modulus

What you get

  • Remainder

💡 Common uses

  • Clock arithmetic.
  • Divisibility checks.
  • Number theory exercises.
  • Computer science and algorithms.

❓ Frequently asked questions

What does modulo mean?

It gives the remainder after division.

Can the modulus be zero?

No. Division by zero is undefined.

Is modulo useful in number theory?

Yes. Congruences and divisibility are commonly expressed using modular arithmetic.