Complete the factor tree with whole numbers to create a factor tree for 72.

Question

72
3^_
3^_
2^_
_^_

Answer 1

To create a factor tree for the number 72 and express it using prime factorization, we can break it down as follows:

1. Start with the number 72.

2. The first step is to factor it into two whole numbers. A simple factor is 8 and 9.

   So we can write:

                72
               /  \
              8    9
   

3. Next, we can factor 8 and 9 further.

   • For 8: it can be factored into 2 and 4 (or 2 * 2 * 2).
   • For 9: it can be factored into 3 and 3 (or 3 * 3).

   Now we have:

                 72
               /    \
              8      9
             / \    / \
            2   4  3   3
               / \
              2   2
   

4. Ultimately, we factor 4 into 2 and 2.

The complete prime factorization of 72 can be expressed as:

\[ 72 = 2^3 \times 3^2 \]

So if we complete your structure, we have:

72
     3^2
       3^_
         2^3
           2^_

In summary, the filled factor tree for 72 with whole numbers looks like:

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

However, in terms of your notation:

72
     3^2
       3^1
         2^3
           2^1