Finding All the Factors of 72 with Factor Pairs

0:00How do you find all the factors of 72, without missing any?

0:05A factor of 72 is a whole number that divides 72 exactly, with no remainder.

0:12A factor pair is two factors that multiply to make 72, such as 6 times 12.

0:19To find them all, test each whole number in order from 1. Does it divide 72 exactly?

0:27Start with 1. 72 divided by 1 is 72, so 1 times 72 is 72.

0:3672 divided by 2 is 36, so 2 times 36 is 72.

0:4372 divided by 3 is 24, so 3 times 24 is 72.

0:5072 divided by 4 is 18, so 4 times 18 is 72.

0:5872 is 5 times 14, remainder 2, so 5 is not a factor.

1:0572 divided by 6 is 12, so 6 times 12 is 72.

1:1272 is 7 times 10, remainder 2, so 7 is not a factor.

1:1872 divided by 8 is 9, so 8 times 9 is 72.

1:25Next is 9, but 9 is already in the list. The pairs have met in the middle, so stop.

1:32Any factor above 8 pairs with a number of 8 or less, so it is already in the list.

1:39Read down the left column, then up the right: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

1:546 factor pairs give 12 factors, so 72 has exactly 12 factors.

2:01A common mistake is skipping a number. Skip 4, and you lose the pair 4 and 18.

2:08Another is stopping too early. Stop after 6, and you miss the pair 8 and 9.

2:16So test whole numbers in order from 1, write each factor pair, and stop when the pairs meet in the middle.