Factor Calculator

Enter a whole number to see every number that divides into it exactly, grouped into factor pairs.

Find factors

Factors of 361, 2, 3, 4, 6, 9, 12, 18, 36
Number of factors
9
Factor pairs
1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
Prime factorization
2² × 3²

What is a factor?

A factor (or divisor) of a whole number n is a whole number that divides n with no remainder. Factors come in pairs that multiply to n: for 36 the pairs are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6.

You only need to test divisors up to √n, because every factor larger than √n is paired with one smaller than it. The calculator uses the prime factorization to generate all factors quickly, even for large numbers.

Worked example

Factors of 36

  1. √36 = 6, so test 1 to 6
  2. 1, 2, 3, 4 and 6 divide 36 exactly; 5 does not
  3. Pair each with 36 ÷ it: 36, 18, 12, 9, 6

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 (nine factors).

Counting factors

If n = pa × qb × …, the number of factors is (a + 1)(b + 1)… For 36 = 2² × 3², that is 3 × 3 = 9. A number has an odd number of factors exactly when it is a perfect square.

Uses

  • Arranging items into equal rows (36 chairs can go in 4 rows of 9 or 6 rows of 6).
  • Simplifying fractions and ratios.
  • Finding the greatest common factor or least common multiple.

Common questions

Do negative numbers have factors?

Yes — −36 has the same positive factors as 36, and each can also be negated. The calculator lists the positive factors, which is the usual convention.

What are the factors of 0?

Every non-zero whole number divides 0, so 0 has infinitely many factors. The calculator asks for a non-zero number for that reason.