All of the factors of a number are contained within the prime factorization in various combinations.
The prime factorization of 210 is 2 x 3 x 5 x 7. If I gave you the number 6 (2 x 3) you would know that the other number in the factor pair is the other two numbers, 5 x 7 or 35. If I gave you 15 (3 x 5) you would be able to find 14 (2 x 7)
Cover up whatever number you have. The numbers that are left are the other factor.
Example: The prime factorization of 72 is 2 x 2 x 2 x 3 x 3
If your first factor is 4, cover up two of the twos. 2 x 3 x 3, or 18, is left.
(18,4) is one factor pair of 72.
The prime factorization.
You do a factor rainbow to find a prime factorization. You compare prime factorizations to find a greatest common factor.
factor tree
With a factor tree, yes.
If completed correctly, the bottom branch of a factor tree will be the prime factorization of the number at the top.
2x2x222
A factor tree
1
Find the prime factorization. Identify the distinct prime factors. Add them up.
The prime factorization of 52 is: 2 x 2 x 13
15 23
22 2,11