1344 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 = 26 x 3 x 7.
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26 x 3 x 7 = 1344
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.