600 = 2*2*2*3*5*5.
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2*2*2*3*5*5 = 600
600 = 2 * 2 * 2 * 3 * 5 * 5 = 23 * 3 * 52
2^7 x 3 x 5^2
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.