Because if all the factors are prime, the factorization can't be broken down further.
Consider some factor strings for 210:
2 x 105
2 x 3 x 35
2 x 3 x 5 x 7
The last (and longest) is the prime factorization.
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The longest string of prime factors for 30 is 2 x 3 x 5 because there isn't a prime factor string that's longer.
All of the factors are prime.
The number of numbers in the string; how long it is.
All of the factors are prime.
The longest factor string is the prime factorization