588 = 2 x 2 x 3 x 7 x 7
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22 x 3 x 72 = 588
22 x 3 x 72 = 588
The prime factors of 588 are 2, 2, 3, 7, 7.
No, 3x5x4 is not a prime factorization of 60. A prime factorization of 60 would consist of only prime numbers. The prime factorization of 60 is 2x2x3x5.
When all the factors are prime numbers, that's a prime factorization.