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

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Answer 1

To create a factor tree for the number 72, we start by finding its prime factors.

1. Divide 72 by the smallest prime number, which is 2: \[ 72 ÷ 2 = 36 \]

2. Next, we can keep breaking down the factors. Since 36 is also even, we divide by 2 again: \[ 36 ÷ 2 = 18 \]

3. Repeat the process with 18: \[ 18 ÷ 2 = 9 \]

4. Now, we have 9, which is not divisible by 2, so we move to the next smallest prime number, which is 3: \[ 9 ÷ 3 = 3 \]

5. Finally, we can divide 3 by itself: \[ 3 ÷ 3 = 1 \]

The complete factor tree for 72 can be represented as follows:

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

In prime factor form, 72 = \( 2^3 \times 3^2 \).