WebTools

Maths

Factor Calculator

List every factor and factor pair of a whole number, with the count, sum and kind.

By Nitin Raturi · Last reviewed

Your number

How to use the Factor Calculator

List every factor of a whole number and its factor pairs.

  1. Enter the number.
  2. Read how many factors it has and what they add up to.
  3. Scan the full list and the factor pairs.

Good to know

  • A number is perfect when its other factors sum to itself, like 28.
  • For prime powers, use the Prime Factorization Calculator.

Number

The whole number whose factors you want.

How to fill it in

  • Enter 1 to 10¹². Short forms such as 1L work.

Example

360 has 24 factors, adding up to 1,170.

Tip: 28 is perfect: its other factors add up to 28. 97 is prime, with only 2 factors; 36 is a square, so it has an odd number (9).

Factors of 360

24 factors

360 has 24 factors that add up to 1,170. It is abundant: its other factors add up to more than the number.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

1 × 360
360
2 × 180
360
3 × 120
360
4 × 90
360
5 × 72
360
6 × 60
360
8 × 45
360
9 × 40
360
10 × 36
360
12 × 30
360
15 × 24
360
18 × 20
360

Positive whole-number factors, including 1 and the number itself.

ChangelogHow we test this calculatorEmbed this calculator

How this calculator works

  1. Step 1Prime factors360 = 2³ × 3² × 5Break the number into primes.
  2. Step 2Combine4 × 3 × 2 = 24Every mix of the prime powers is a factor.
  3. Step 3Pair upa × b = nEach factor below √n pairs with one above.

A factor divides the number with no remainder. The calculator builds them all from the prime factors, so even 12-digit numbers are instant.

Worked example: 360

The first factor pairs of 360
Count
(3 + 1)(2 + 1)(1 + 1) = 24
  1. 1 × 360360
  2. 2 × 180360
  3. 3 × 120360
  4. 4 × 90360
  5. 5 × 72360
  6. 6 × 60360
  7. All factors24, summing to 1,170

360 has more factors than any smaller number, which is one reason a circle has 360 degrees.

Prime, square or perfect

  • 972 factorsPrime: only 1 and itself.
  • 369 factorsSquare: 6 × 6 pairs with itself, so the count is odd.
  • 28sum 561 + 2 + 4 + 7 + 14 = 28: a perfect number.

Only perfect squares have an odd number of factors.

Assumptions and limits

  • Positive factorsIncluding 1 and the number itself.
  • Up to 10¹²Counts and sums are always complete.
  • 500 listedLonger lists are cut short on screen.
  • No negativesNegative factors are not shown.

Factors list every divisor. Prime factors, LCM and HCF are built from them.

For the prime building blocks, use the prime factorization calculator. To find common factors and multiples of several numbers, try the LCM and HCF calculator.

Common mistakes

  • Mistake: Forgetting 1 and the number itself.

    Instead: Both are always factors.

  • Mistake: Stopping halfway.

    Instead: Check up to √n; each find gives a pair.

  • Mistake: Confusing factors with multiples.

    Instead: Factors divide n; multiples are divided by n.

Checking the method

A separate script re-works every golden value by trial division up to the square root, without prime factors.

Read how we test our calculators, or browse more maths calculators.

Frequently asked questions

How many factors does 360 have?

24, from 1, 2, 3, 4, 5, 6 up to 360. They add up to 1,170.

What are the factors of 36?

1, 2, 3, 4, 6, 9, 12, 18, 36: 9 factors, an odd count because 36 is a square.

What is a perfect number?

One whose other factors add up to itself: 1 + 2 + 4 + 7 + 14 = 28.

How do I know a number is prime?

It has exactly two factors. 97 has only 1 and 97.

How are factor pairs found?

Check each number up to the square root; every one that divides gives a pair.

Sources and methodology

The formulas are standard time-value-of-money results. We check every figure against golden values worked out independently, by closed form and by month-by-month simulation; see the methodology.

Written and maintained by Nitin Raturi, a software engineer (about the author). Last reviewed 4 Nov 2026; next review due by . Found an error? Tell us.

Changelog

  • : Initial release.