Question
What is the prime factorization of 252?
2 2 · 3 2 · 7
2 2 · 7 · 9
2 · 7 · 27
2 3 · 3 · 7
2 2 · 3 2 · 7
2 2 · 7 · 9
2 · 7 · 27
2 3 · 3 · 7
Answers
GPT-4o mini
To find the prime factorization of 252, we can start by dividing it by the smallest prime numbers:
1. Divide by \(2\):
\[
252 \div 2 = 126
\]
2. Divide by \(2\) again:
\[
126 \div 2 = 63
\]
3. Now, divide by \(3\):
\[
63 \div 3 = 21
\]
4. Divide by \(3\) again:
\[
21 \div 3 = 7
\]
5. Lastly, divide by \(7\):
\[
7 \div 7 = 1
\]
Putting that all together, we find that:
\[
252 = 2^2 \cdot 3^2 \cdot 7
\]
Therefore, the prime factorization of 252 is:
\[
2^2 \cdot 3^2 \cdot 7
\]
This corresponds to the first option in your list:
**\(2^2 \cdot 3^2 \cdot 7\)**.
1. Divide by \(2\):
\[
252 \div 2 = 126
\]
2. Divide by \(2\) again:
\[
126 \div 2 = 63
\]
3. Now, divide by \(3\):
\[
63 \div 3 = 21
\]
4. Divide by \(3\) again:
\[
21 \div 3 = 7
\]
5. Lastly, divide by \(7\):
\[
7 \div 7 = 1
\]
Putting that all together, we find that:
\[
252 = 2^2 \cdot 3^2 \cdot 7
\]
Therefore, the prime factorization of 252 is:
\[
2^2 \cdot 3^2 \cdot 7
\]
This corresponds to the first option in your list:
**\(2^2 \cdot 3^2 \cdot 7\)**.