Find the number of factors of 100?A] 7                             B] 2                             C] 6                 D] 9Options :ABCD

1. Break Down the Problem

To find the number of factors of 100, we start by determining its prime factorization.

2. Relevant Concepts

The formula for finding the number of factors of a number based on its prime factorization is: $(n_1 + 1)(n_2 + 1)(n_3 + 1)...(n_k + 1)$ where $n_1, n_2, n_3, ..., n_k$ are the exponents in the prime factorization.

3. Analysis and Detail

1. Prime Factorization of 100:

   • The prime factorization of 100 is $100 = 10^2 = (2 \times 5)^2 = 2^2 \times 5^2$.

2. Identifying the Exponents:

   • In this case, we have:
     • For $2^2$, the exponent is 2.
     • For $5^2$, the exponent is 2.

3. Applying the Formula:

   • Using the formula, we calculate the number of factors: $(2 + 1)(2 + 1) = 3 \times 3 = 9$

4. Verify and Summarize

We verify the calculations to ensure accuracy. The prime factorization is correct, and applying the factor formula gives a consistent and correct result.

Final Answer

The number of factors of 100 is $9$, therefore the correct option is D.