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.

Related questions
See all questions in Prime Factorization
Impact of this question
12049 views around the world
You can reuse this answer
Creative Commons License