Question

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

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
```