Factor calculator

What a factor is

A factor of a number divides it exactly, with nothing left over. The factors of 12 are 1, 2, 3, 4, 6 and 12. Factors come in pairs that multiply to the number: 1 × 12, 2 × 6 and 3 × 4.

How the page finds them

It tries every whole number from 1 up to the square root of your number. Each one that divides exactly gives a pair: the number itself and the answer of the division. There is no need to go past the square root, because the second number of every pair is above it. For 360 the square root is about 18.97, so the page tries 1 to 18 and finds 12 pairs, 24 factors in all.

Prime factorization

Every whole number above 1 can be written as a product of primes in exactly one way. 360 = 2³ × 3² × 5, meaning 2 × 2 × 2 × 3 × 3 × 5. The page finds this by dividing by 2 as many times as it can, then 3, then 5, and so on.

Counting factors from the primes

Add 1 to each power in the prime factorization and multiply. For 360 that is (3 + 1) × (2 + 1) × (1 + 1) = 24, which matches the list.

Limits

The page handles whole numbers from 1 to one trillion (1,000,000,000,000). Negative numbers have the same factors with a minus sign, and 0 is left out because every number divides it. To test only whether a number is prime, use the prime number checker.