This is because a factor is defined in terms of multiplication, not addition. One integer, p, is a factor of another integer, q, if there is some integer, r (which is not equal to 1) such that p*r = q.
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45 Divide by three. 15,3 Divide by three. 5,3,3 Stop.
36 18,2 9,2,2 3,3,2,2 2 x 2 x 3 x 3 = 36
If you construct them correctly, factor trees always work to determine the prime factorization of a number. Once you compare the prime factorizations of two or more numbers, it is relatively easy to find the greatest common factor of them from there.
44 Divide by two. 22,2 Divide by two. 11,2,2 Stop. 2 x 2 x 11 = 44
100 50,2 25,2,2 5,5,2,2