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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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How are the factors 36 and 72 related?
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. All of the factors of 36 are also factors of 72.
How are factors of 36 related to the factors of 72?
Since 36 is a factor of 72, all of its factors are included in the factors of 72.
What is the common factor for 18 72?
Since 18 is a factor of 72, all of its factors are common.
Is 6 factor of 72?
Divide 6 into 72. If the answer has no remainder, 6 is a factor.
What factors do 64 and 72 have in common?
Since 24 is a factor of 72, all of its factors are common.
