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Factor Calculator

Find all the factors of a whole number, list its factor pairs, get its prime factorization and see whether it's prime.

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Calculator

Up to 1,000,000,000,000.

Factors of 360

24 factors

Prime factorization

2³ × 3² × 5

Is it prime?

No

All factors

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

Factor pairs (12)

1 × 360

2 × 180

3 × 120

4 × 90

5 × 72

6 × 60

8 × 45

9 × 40

10 × 36

12 × 30

15 × 24

18 × 20

A factor (or divisor) of n is a whole number that divides n with no remainder. Factors come in pairs whose product is n.

Keep analyzing

For estimates only. Double-check the numbers before making important decisions.

What factors are

A factor (or divisor) of a number is a whole number that divides it evenly, with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12. They come in factor pairs that multiply to 12: 1 × 12, 2 × 6 and 3 × 4.

Prime factorization

Every whole number greater than 1 can be written in exactly one way as a product of prime numbers. From that prime factorization you can build every factor and count how many there are.

n = p₁^a × p₂^b × …
Number of factors = (a + 1) × (b + 1) × …
360 = 2³ × 3² × 5 → (3 + 1)(2 + 1)(1 + 1) = 24 factors

How to read the result

  • Exactly two factors (1 and the number itself): the number is prime.
  • More than two factors: the number is composite.
  • An odd number of factors: the number is a perfect square, because one pair repeats (36 has 9 factors, including 6 × 6).
  • The number 1 has only one factor and is neither prime nor composite.

How large a number you can enter

The calculator works with positive whole numbers up to 1 trillion (1,000,000,000,000).

Example

The number 360 has 24 factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360. They form 12 factor pairs, from 1 × 360 to 18 × 20, and the prime factorization is 2³ × 3² × 5.

  1. 360 = 2 × 180 = 2 × 2 × 90 = 2 × 2 × 2 × 45
  2. 45 = 3 × 3 × 5
  3. 360 = 2³ × 3² × 5
  4. (3 + 1) × (2 + 1) × (1 + 1) = 24 factors

Common mistakes

  • Leaving out 1 and the number itself: both are always factors.
  • Confusing factors with multiples: factors divide the number (4 is a factor of 12), while multiples are the number times something (24 is a multiple of 12).
  • Stopping too early when listing factor pairs: you only need to test up to the square root, but you have to test every number up to it.

Frequently asked questions

How do you find all the factors of a number?

Divide the number by 1, 2, 3 and so on up to its square root. Each divisor that leaves no remainder gives you a factor pair. For 36, testing 1 through 6 gives 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6.

How do you know how many factors a number has?

Write its prime factorization, add 1 to each exponent and multiply. For 360 = 2³ × 3² × 5: 4 × 3 × 2 = 24 factors.

What are factor pairs used for?

They're pairs of numbers that multiply to the original number. For example, they give you every whole-number length and width for a rectangle with a given area.

Is 1 a prime number?

No. A prime number has exactly two factors, 1 and itself. The number 1 has only one factor, so it is neither prime nor composite.

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