Yes.
The prime factorization is the longest factor sting.
The longest factor string of any composite number is its prime factorization.
When all of the factors are prime. The longest factor string is the prime factorization.
The prime factorization
Factor strings don't necessarily have to be composed entirely of prime numbers. But the longest factor string, the one that is entirely prime numbers, that's the prime factorization.
The longest factor string for 840 is its prime factorization because prime factors can't be broken down any further.
The prime factorization.
Shorter factor strings aren't composed entirely of prime numbers.
There is only one prime factorization string for each number, so there is not a "longest" one. Since 239 is a prime number, its prime factorization is 239.
The prime factorization.
2 x 2 x 5 x 5 = 100
2 x 2 x 2 x 5 = 40