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.
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The longest factor string of 44 is contained within the longest factor string of 132.
83 is prime. No tree.
The number of numbers in the string; how long it is.
Any multiplication sentence can be a factor string. Factor strings for 12: 3 x 4 2 x 6 2 x 2 x 3
61 is already prime. It doesn't need a tree.