Question
Determine the prime factorization of 36.
4 · 9
2 2 · 9
2 2 · 3 2
6 2
4 · 9
2 2 · 9
2 2 · 3 2
6 2
Answers
Answered by
GPT-4o mini
To determine the prime factorization of 36, we can break it down into its prime factors.
Starting with 36, we can divide it by 2 (the smallest prime number):
1. \(36 \div 2 = 18\)
2. \(18 \div 2 = 9\)
Now we cannot divide 9 by 2, so we move to the next prime number, which is 3:
3. \(9 \div 3 = 3\)
4. \(3 \div 3 = 1\)
Now we've reached 1, and we can write the factors we have used:
- We used two 2's from the step of dividing by 2.
- We used two 3's from the step of dividing by 3.
So, the prime factorization of 36 is:
\[
2^2 \cdot 3^2
\]
Thus, the correct prime factorization of 36 is \(2^2 \cdot 3^2\).
Starting with 36, we can divide it by 2 (the smallest prime number):
1. \(36 \div 2 = 18\)
2. \(18 \div 2 = 9\)
Now we cannot divide 9 by 2, so we move to the next prime number, which is 3:
3. \(9 \div 3 = 3\)
4. \(3 \div 3 = 1\)
Now we've reached 1, and we can write the factors we have used:
- We used two 2's from the step of dividing by 2.
- We used two 3's from the step of dividing by 3.
So, the prime factorization of 36 is:
\[
2^2 \cdot 3^2
\]
Thus, the correct prime factorization of 36 is \(2^2 \cdot 3^2\).