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To factor 72, we divide by successive prime numbers until we end up with 1:

72 / 2 = 36 (still divisible by 2)
36 / 2 = 18 (still divisible by 2)
18 / 2 = 9 (not divisible by 2, try 3)
9 / 3 = 3 (still divisible by 3)
3 / 3 = 1 (at 1, done factoring)


so, in simplest form, 72 factors to:


2 x 2 x 2 x 3 x 3 or 2^3 x 3^2


To see all of the factors, one creates unique combinations of all factors above, including 1 and the number itself:


1
2
3
2 x 2 = 4
2 x 3 = 6
2 x 2 x 2 = 8
3 x 3 = 9
2 x 2 x 3 = 12
2 x 3 x 3 = 18
2 x 2 x 2 x 3 = 24
2 x 2 x 3 x 3 = 36
72

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1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

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13y ago
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Q: Find all of the factors of 72?
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