Factors Calculator

This factors of a number calculator lists every factor of any whole number in seconds. Type in a number and you get all of its factors, the factor pairs, and the step-by-step working that found them. Students use it to check divisibility homework, teachers use it to build factor exercises, and anyone simplifying a fraction can spot the common factors at a glance.

How factors are found

The calculator uses trial division. It tests every whole number i from 1 up to the square root of your number. Whenever the division leaves no remainder, both i and the matching quotient are factors. Because factors come in pairs, testing up to the square root is enough: every factor larger than the square root already appeared as the partner of a smaller one.

Worked example: factors of 18

  1. The square root of 18 is about 4.24, so only 1, 2, 3 and 4 need testing.
  2. 18 ÷ 1 = 18, so 1 and 18 are factors.
  3. 18 ÷ 2 = 9, so 2 and 9 are factors.
  4. 18 ÷ 3 = 6, so 3 and 6 are factors.
  5. 18 ÷ 4 does not divide evenly, so 4 is not a factor.
  6. The full set is 1, 2, 3, 6, 9 and 18: six factors in three pairs.

How to use this calculator

  1. Type a whole number into the labelled box.
  2. Press Find factors or hit Enter.
  3. Read the factor list, the factor pairs and the working shown underneath.

Limits of this tool

  • The box accepts positive whole numbers only. Decimals, letters, zero and negative numbers show a clear error message.
  • Numbers above 100,000,000 are rejected to keep the tool fast in your browser.
  • The tool finds the factors of one number at a time. To compare two numbers, run each one separately.
  • All the maths happens in your browser, so your numbers never leave your device.

Frequently asked questions

What is the difference between a factor and a multiple?

A factor divides a number evenly: 3 is a factor of 12. A multiple is what you get by multiplying: 24 is a multiple of 12. Factors are always the same size as the number or smaller; multiples grow without limit.

Is 1 a factor of every number?

Yes. Every whole number divides evenly by 1, and 1 times the number gives the number itself. That is why (1, 18) is always the first factor pair in the working.

Can this factors of a number calculator handle large numbers?

It works well up to 100,000,000. Above that the tool asks for a smaller number, because testing every possible divisor would take too long in a browser.

What is a factor pair?

Two whole numbers that multiply to give your number. For 18 the pairs are (1, 18), (2, 9) and (3, 6). Every factor belongs to exactly one pair.

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