The only name is factorization.
Not really. A factor string is a multiplication sentence. A factor tree is a way of notating the process of finding the prime factorization of a given number. End result: 4 x 9 can be a factor string for 36, but can't be a prime factorization. The prime factorization of 36 is 2 x 2 x 3 x 3.
When you want to find the prime factorization of a composite number.
if its a math one i say prime factorization.
Divide prime numbers into it. Start with 2. Do that four times. Then try 3. Stop.
The prime factorization.
2x2x222
51 3,17
by using a prime factor tree
88 44,2 22,2,2 11,2,2,2
It is: 3*17 = 51
27 9,3 3,3,3
956 478,2 239,2,2
52 26,2 13,2,2
92 46,2 23,2,2
28 14,2 7,2,2
That's prime factorization. 45 15,3 5,3,3