72 = 23 × 32
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Since 72 is a factor of 144, its entire prime factorization will be contained in the prime factorization of 144.
there is no prime factorization of 72 except for 1 and 72
72 36,2 18,2,2 9,2,2,2 3,3,2,2,2
Since 36 is a factor of 72, it will have everything in common with it.
To find the prime factorization, start with any two factor pairs of a number and factor until all factors are prime. 2 x 36 = 72 2 x 2 x 18 2 x 2 x 2 x 9 2 x 2 x 2 x 3 x 3 is the prime factorization of 72.