# 324 Christmas Factor Trees

• 324 is a composite number.
• Prime factorization: 324 = 2 x 2 x 3 x 3 x 3 x 3, which can be written 324 = (2^2) x (3^4)
• The exponents in the prime factorization are 2 and 4. Adding one to each and multiplying we get (2 + 1)(4 + 1) = 3 x 5 = 15. Therefore 324 has exactly 15 factors.
• Factors of 324: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
• Factor pairs: 324 = 1 x 324, 2 x 162, 3 x 108, 4 x 81, 6 x 54, 9 x 36, 12 x 27, or 18 x 18
• 324 is a perfect square. √324 = 18

Included in these 324 factor trees are smaller factor trees for the numbers in brown: 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, and 162. Prime factors of 324 are in red.

This Level 2 puzzle looks like part of a Christmas tree branch. It’s not too difficult to solve. Give it a try!

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-15

## 2 thoughts on “324 Christmas Factor Trees”

1. I’m really enjoying the seasonal flair that you are giving to the puzzles. It was interesting for me to realize that it was your integration of playful, colorful elements that lured me into figuring out what the puzzles were all about. I hope you’ve been enjoying making them as much as I’ve been enjoying seeing them.
I’m off to bed now, pleased to know that 324 is a perfect square.

2. I’m glad you’re enjoying them. It’s been fun to add a little color for the holidays.

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