Question
What is the prime factorization of 72?
22 × 32
22 × 33
23 × 32
23 × 33
22 × 32
22 × 33
23 × 32
23 × 33
Answers
GPT-4o mini
To find the prime factorization of 72, we can divide it by the smallest prime numbers.
1. Divide by 2:
\( 72 \div 2 = 36 \)
2. Divide by 2 again:
\( 36 \div 2 = 18 \)
3. Divide by 2 again:
\( 18 \div 2 = 9 \)
4. Divide by 3:
\( 9 \div 3 = 3 \)
5. Divide by 3 again:
\( 3 \div 3 = 1 \)
Now we can express 72 as the product of its prime factors. Counting the factors:
- We divided by 2 three times → \( 2^3 \)
- We divided by 3 twice → \( 3^2 \)
Therefore, the prime factorization of 72 is:
\[
72 = 2^3 \times 3^2
\]
So, the correct answer from the options provided is:
\( 2^3 \times 3^2 \) (which corresponds to the option \( 23 \times 32 \)).
1. Divide by 2:
\( 72 \div 2 = 36 \)
2. Divide by 2 again:
\( 36 \div 2 = 18 \)
3. Divide by 2 again:
\( 18 \div 2 = 9 \)
4. Divide by 3:
\( 9 \div 3 = 3 \)
5. Divide by 3 again:
\( 3 \div 3 = 1 \)
Now we can express 72 as the product of its prime factors. Counting the factors:
- We divided by 2 three times → \( 2^3 \)
- We divided by 3 twice → \( 3^2 \)
Therefore, the prime factorization of 72 is:
\[
72 = 2^3 \times 3^2
\]
So, the correct answer from the options provided is:
\( 2^3 \times 3^2 \) (which corresponds to the option \( 23 \times 32 \)).