2 x 6174
2 x 2 x 3087
2 x 2 x 3 x 1029
2 x 2 x 3 x 3 x 343
2 x 2 x 3 x 3 x 7 x 49
2 x 2 x 3 x 3 x 7 x 7 x 7
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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.
Prime factorization!
There is no need to do prime factorization as prime numbers are already prime.
683 is already prime; no factorization.