Question
What is the prime factorization of 36?
A.
6 · 3 · 2
B.
22 · 9
C.
4 · 32
D.
22 · 32
A.
6 · 3 · 2
B.
22 · 9
C.
4 · 32
D.
22 · 32
Answers
GPT-4o mini
To find the prime factorization of 36, we can break it down into its prime factors.
1. Start with 36:
\( 36 = 6 \times 6 \)
2. We can further factor 6:
\( 6 = 2 \times 3 \)
3. So, we can rewrite both 6s:
\( 36 = 6 \times 6 = (2 \times 3) \times (2 \times 3) \)
4. This means:
\( 36 = 2^2 \times 3^2 \)
Now let's check the provided options:
A. \( 6 \cdot 3 \cdot 2 \) (not in prime factorization)
B. \( 2^2 \cdot 9 \) (not in proper prime factorization)
C. \( 4 \cdot 3^2 \) (4 is not prime)
D. \( 2^2 \cdot 3^2 \) (this is the correct prime factorization)
Thus, the correct answer, in terms of proper prime factorization, is \( 36 = 2^2 \cdot 3^2 \), but none of the options are correct representations of this.
If you prefer choices, and if option D implies \( 2^2 \cdot 3^2 \), it is the closest to the correct prime factorization based on standard notation.
1. Start with 36:
\( 36 = 6 \times 6 \)
2. We can further factor 6:
\( 6 = 2 \times 3 \)
3. So, we can rewrite both 6s:
\( 36 = 6 \times 6 = (2 \times 3) \times (2 \times 3) \)
4. This means:
\( 36 = 2^2 \times 3^2 \)
Now let's check the provided options:
A. \( 6 \cdot 3 \cdot 2 \) (not in prime factorization)
B. \( 2^2 \cdot 9 \) (not in proper prime factorization)
C. \( 4 \cdot 3^2 \) (4 is not prime)
D. \( 2^2 \cdot 3^2 \) (this is the correct prime factorization)
Thus, the correct answer, in terms of proper prime factorization, is \( 36 = 2^2 \cdot 3^2 \), but none of the options are correct representations of this.
If you prefer choices, and if option D implies \( 2^2 \cdot 3^2 \), it is the closest to the correct prime factorization based on standard notation.