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Modulo Calculator

Modulo Calculator is part of Toolspire and is ready as soon as this page loads. Both numbers must be integers. The divisor cannot be zero. The remainder is always smaller than the absolute value of the divisor and, here, non-negative.

Runs in this tabFreeNo account

On this page

What you can do here

The multiple is in the detail

You can see the quotient that was thrown away.

Negative dividends stay non-negative

The remainder is not JavaScript’s signed % . −17 % 5 is −2 in JavaScript and 3 here.

Integers only

17.5 is not given a remainder. Scale it to an integer problem if you need one.

The sequence

How to use the Modulo Calculator

  1. 1

    Type the number being divided first

    17 mod 5 is dividend 17, divisor 5.

  2. 2

    Check 2

    Three fives are 15, and 17 − 15 is 2.

  3. 3

    Try a negative dividend if you write clock arithmetic

    The remainder should come back at 0 or above.

Worth knowing

  • Modulo Calculator on Toolspire: 17 = 5 × 3 + 2, so 17 mod 5 = 2.
  • The remainder uses the non-negative residue. −17 mod 5 is 3, because −20 is the multiple at or below −17 and the gap is 3.
  • A divisor of 0 is rejected.
  • Decimals are rejected. Modulo on this page is an integer operation.

A remainder you can add back

The useful identity is dividend = quotient × divisor + remainder, with a remainder that is at least 0 and strictly smaller than the divisor’s absolute value. JavaScript’s % operator keeps the sign of the dividend, so −17 % 5 is −2, and −2 does not satisfy that identity with a non-negative remainder. This page uses the non-negative one: −17 = (−4) × 5 + 3.

FAQ

Questions about Modulo Calculator

Where does Modulo Calculator run?

Modulo Calculator runs in this tab on Toolspire. What you type or drop in is not sent to us and is not stored on a server.

What is 17 mod 5?

2. The quotient is 3.

What is −17 mod 5?

3, not −2. −20 + 3 = −17.

What about division by zero?

Rejected. There is no remainder.

Can I use decimals?

No. 17.2 mod 5 is not this tool.

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