Question

Find the prime factorization of 720. Show your work and the factor tree for full points.(3 points)

Answer 1

To find the prime factorization of 720, we can use a factor tree. The process involves dividing the number by the smallest prime numbers until we reach 1. Let's go through the steps together:

1. **Start with the number 720**. We can divide it by 2, the smallest prime number.

\[
720 \div 2 = 360
\]

2. **Continue factoring 360**:

\[
360 \div 2 = 180
\]

3. **Continue with 180**:

\[
180 \div 2 = 90
\]

4. **Continue with 90**:

\[
90 \div 2 = 45
\]

5. **Now we can factor 45**. Since 45 is not even, we'll divide by the next smallest prime, which is 3:

\[
45 \div 3 = 15
\]

6. **Continue with 15**:

\[
15 \div 3 = 5
\]

7. **Finally, we are left with 5**, which is a prime number.

Now we have all the factors:
- 720 can be expressed as \(2^4 \times 3^2 \times 5^1\).

### Prime Factorization
The complete prime factorization is:

\[
720 = 2^4 \times 3^2 \times 5
\]

### Factor Tree
Here’s how the factor tree looks:

```
720
/ \
2 360
/ \
2 180
/ \
2 90
/ \
2 45
/ \
3 15
/ \
3 5
```

### Conclusion
The prime factorization of 720 is \(2^4 \times 3^2 \times 5\).