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.
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
The prime factorization.
The prime factorization.
2x3x5
When all of the factors are prime. The longest factor string is the prime factorization.
Because 1 isn't prime.
When all the factors are prime.
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.
Find the prime factors first.
The longest factor string for 840 is its prime factorization because prime factors can't be broken down any further.
the longest string of prime factor for 30 is 2 x 3 x 5
All of the factors are prime.
For composite numbers, only one string of factors is the longest; the prime factorization.