Complete the factor tree with whole numbers to create a factor tree for 72. (2 points)

Question

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Remaining Attempts : 3

Answer 1

To create a factor tree for 72, we break it down into its prime factors. Here’s how it can be done step by step:

1. Start with 72 at the top.
2. Divide 72 by 2 (the smallest prime number):
   • 72 ÷ 2 = 36
3. Now, take 36, and divide it by 2 again:
   • 36 ÷ 2 = 18
4. Take 18, and divide it by 2:
   • 18 ÷ 2 = 9
5. Now, take 9, which is not divisible by 2, and divide it by 3 (the next smallest prime):
   • 9 ÷ 3 = 3
6. Lastly, divide 3 by 3:
   • 3 ÷ 3 = 1

Now, you can write the factor tree as follows:

          72
         /  \
       2    36
           /  \
          2    18
              /  \
             2    9
                 / \
                3   3

The prime factors of 72 are \(2 \times 2 \times 2 \times 3 \times 3\), or \(2^3 \times 3^2\).