Factor Pairs

Every factor has a partner. Since 4 × 9 is 36, 4 and 9 are a factor pair of 36: two numbers that multiply to it. To list every factor of 36, find every pair, testing 1, 2, 3 and so on in order.

1, 2, 3 and 4 all divide 36, giving 1 × 36, 2 × 18, 3 × 12 and 4 × 9. 5 leaves 1 over, so it has no partner. Then 6 × 6: the two numbers of the pair are equal, so the pairs have met and you stop. Any pair after this one would be an old pair turned around, like 9 and 4.

So the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Working in pairs is what keeps this quick: you only test small numbers, and each one that divides hands you a big partner for free.