13 is already prime. It doesn't need a tree.
56 28,2 14,2,2 7,2,2,2
484 242,2 121,2,2 11,11,2,2
126 ^ 9 14 ^ ^ 3 3 7 2
675 225,3 75,3,3 25,3,3,3 5,5,3,3,3
126 63,2 21,3,2 7,3,3,2
126 63,2 21,3,2 7,3,3,2
126 63,2 21,3,2 7,3,3,2
126 63,2 21,3,2 7,3,3,2
126 63,2 21,3,2 7,3,3,2
2,3,3,7
Factor tree:126|63 and 2|21 and 32 x 3 x 21 = 126
77 7,11
15 3,5
1,270,2,135
23 is a prime number. No prime factorization. No tree.
13 is already prime. It doesn't need a tree.