All factors calculator

List all factors of any number. Shows every divisor, factor pairs, and total count.

Number

What are factors?

Factors (or divisors) of n are all positive integers that divide n evenly. For 12, the factors are: 1, 2, 3, 4, 6, 12.

Finding factors

Test each integer from 1 to √n. If i divides n, both i and n/i are factors. For 36: test 1→6. Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factor pairs

Factors come in pairs that multiply to give n. For 36: (1,36), (2,18), (3,12), (4,9), (6,6). The square root separates the "small" and "large" factors.

Number of factors formula

If n = p₁^a₁ × p₂^a₂ × ..., then the total number of factors = (a₁+1)(a₂+1)... For 360 = 2³×3²×5: factors = 4×3×2 = 24.