To determine the prime factorization of 36, we break it down into its prime factors step-by-step.
1. Starting with 36:
36 is an even number, so we start by dividing it by the smallest prime number, which is 2.
[tex]\[ 36 ÷ 2 = 18 \][/tex]
2. Now we have 18:
18 is also an even number, so we divide by 2 again.
[tex]\[ 18 ÷ 2 = 9 \][/tex]
3. Next, we have 9:
9 is not an even number, so we check the next smallest prime, which is 3.
[tex]\[ 9 ÷ 3 = 3 \][/tex]
4. Finally, we have 3:
3 is a prime number, so we divide by 3 again.
[tex]\[ 3 ÷ 3 = 1 \][/tex]
So, we've used the primes 2, 2, 3, and 3. Therefore, the prime factorization of 36 is:
[tex]\[ 2 \times 2 \times 3 \times 3 \][/tex]
Thus, out of the given options, the correct one showing the prime factorization of 36 is:
[tex]\[ 2 \times 2 \times 3 \times 3 \][/tex]
