How many numbers of prime factors does 36 have?

• A. 4
• B. 3
• C. 2
• D. 1

To determine how many prime factors the number 36 has, we first need to break it down into its prime factorization. Prime factors are the prime numbers that multiply together to give the original number. Let's go through the steps to find the prime factors of 36.

Finding the Prime Factorization of 36

We start by dividing 36 by the smallest prime number, which is 2:

• 36 ÷ 2 = 18
• 18 ÷ 2 = 9

Now, we can no longer divide by 2 since 9 is not even. The next prime number is 3:

• 9 ÷ 3 = 3
• 3 ÷ 3 = 1

Now that we have reached 1, we can compile the prime factors we used:

List of Prime Factors

The prime factors of 36 are:

• 2 (used twice)
• 3 (used twice)

Counting the Unique Prime Factors

While we have the prime factors 2 and 3, we need to count only the unique prime factors. In this case, the unique prime factors of 36 are:

• 2
• 3

Thus, there are two unique prime factors of 36. Therefore, the answer to the question is:

Final Answer

The correct choice is C. 2.

In summary, when we factor 36, we find that it can be expressed as \(2^2 \times 3^2\). This shows that while the number of times each prime factor appears is important, we only count the distinct primes when asked for the number of prime factors. So, 36 has two unique prime factors: 2 and 3.