It's done by dividing your target number by prime numbers until all the factors are prime. Some people use factor trees, rainbows, ladders, fireworks, etc. as visual aids.
Example 210:
210
105,2
35,3,2
7,5,3,2
The prime factorization of 210 is 2 x 3 x 5 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.
the prime factorization of 2x2x13x17 is 884