672 is an even number, so it divides by 2. Do this.
672/2 = 336. Also even, so divide by two.
336/2 = 168. Also even, so divide by two.
168/2 = 84. divide by 2
84/2 = 42. divide by 2.
42/2 = 21. 21 is not even. Does it divide by 3 ? Bingo !!
count up the twos above - 5 of them.
So, 672 = 2x2x2x2x2x3x7.
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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
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.