Find the smallest number which when divided by 8 and 12 leaves no remainder.

To find every factor of a number, walk up from 1 and check each whole number — if it divides the number with no remainder, it is a factor. Factors come in **pairs**: if 4 is a factor of 12, so is 12 ÷ 4 = 3. So you only need to check up to the square root of the number to find them all. Factors of 12: $1\times 12,2\times 6,3\times 4$ — six factors total: 1, 2, 3, 4, 6, 12. Every number has 1 and itself as factors.