In the prime factorization of 132, if it is 2 times 2 times 3 times X, what is the value of X?

• A. 5
• B. 7
• C. 11
• D. 13

Answer: (C)

To find the value of X in the prime factorization of 132, let's start with the complete factorization of 132.

First, we can divide 132 by the smallest prime number, which is 2. This gives us:

132 ÷ 2 = 66.

We can apply the division by 2 again, since 66 is also even:

66 ÷ 2 = 33.

Now, we are left with 33, which is no longer divisible by 2. The next smallest prime number is 3:

33 ÷ 3 = 11.

At this point, we have 11 remaining, which is also a prime number. Thus, the complete prime factorization of 132 can be expressed as:

2 × 2 × 3 × 11.

In the context of the question, we see that 2 times 2 times 3 times X must match this factorization. From our complete breakdown, it is clear that X corresponds to the leftover prime factor of 11.

Therefore, the value of X is 11.