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 \(2^4 \times 3^2 \times 5\).