Divide 672 by 2 five times until you get to 21.
672
336,2
168,2,2
84,2,2,2
42,2,2,2,2
21,2,2,2,2,2
7,3,2,2,2,2,2
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In actual fact, the prime factorization of 42 is not 21 x 2, as 21 is not a prime number. The complete prime factorization of 42 is 2 x 3 x 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.
Prime factorization!
There is no need to do prime factorization as prime numbers are already prime.