How do you write the factor trees for 24?

1 Answer
Geoff K.
Nov 18, 2016

Keep "breaking off" prime pieces until you can't do it anymore.

Explanation:

#"       24"#               24 is even; we can take out a factor of 2.
#"      /  \"#
#"     2   12"#            12 is also even; take out another 2.
#"         /  \"#
#"        2    6"#         6 is again even, so we take out another 2.
#"            /  \"#
#"           2    3"#      3 is prime. We are done.

The prime factorization of #24# is the product of all the "nodes" of the tree. In this case,

#24=2times2times2times3#, or
#24=2^3times3#

The final factor tree can be written as above, or it can be written with all the nodes carried down to the bottom line:

#"       24"#
#"      /  \"#
#"     2   12"#
#"    /   /  \"#
#"   2   2    6"#
#"  /   /    / \"#
#" 2   2    2   3"#

This takes more time, but it is easier to find all the nodes, because they're all on the bottom row.

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