You break down the factors of a number until all the factors are prime.
For example:
24
/ \
6 4
/ \
3x2 x 2x2
This factor tree was very easy, but there will be harder ones in the future. When all the numbers at the bottom of the tree are prime, you are finished. Factor trees may also be used to find the prime factorization of a number. PS: I'm sorry about the appearance of the tree. Once I published it, it became, and stayed that way. Real factor trees don't look like this. 24 is broken down into 6x4, because they are the factors. Since 24 is composite, you do not have to use 6x4. Then we break 6 into 3x2, and 4 into 2x2. Then 3x2x2x2 is a prime factorization. And you are also done with the factor tree!
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You need at least two factor trees to find a GCF.
Find out about factors and factor trees.
Since prime numbers only have one prime factor (themselves), factor trees are unnecessary.
44 11.4 11,2,2
44 22,2 11,2,2