8. Which of the following shows the prime factorization for 720 ? A. (O) $$ 2^{4} imes 3^{2} imes 5 $$

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8. Which of the following shows the prime factorization for 720 ? A. (O) $$ 2^{4} 	imes 3^{2} 	imes 5 $$

UpStudy AI · Accepted Answer

To find the prime factorization of 720, we can break it down step by step.

1. **Divide by the smallest prime number (2):**
   - $$ 720 \div 2 = 360 $$
   - $$ 360 \div 2 = 180 $$
   - $$ 180 \div 2 = 90 $$
   - $$ 90 \div 2 = 45 $$

2. **Now, 45 is not divisible by 2, so we move to the next prime number (3):**
   - $$ 45 \div 3 = 15 $$
   - $$ 15 \div 3 = 5 $$

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

Now, we can summarize the prime factors we found:
- From the divisions by 2, we have $$ 2^4 $$ (since we divided by 2 four times).
- From the divisions by 3, we have $$ 3^2 $$ (since we divided by 3 two times).
- Finally, we have $$ 5^1 $$ (since we have one factor of 5).

Putting it all together, the prime factorization of 720 is:
$$
720 = 2^4 \times 3^2 \times 5^1
$$

Thus, the correct answer is:
A. $$ 2^{4} \times 3^{2} \times 5 $$
The prime factorization of 720 is $$ 2^{4} \times 3^{2} \times 5 $$.

Which of the following shows the prime factorization for 720 ?
A. (O)

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