Question

How many distinct prime factors are there in 9900?

• A. \(7\)
• B. \(4\)
• C. \(11\)
• D. \(5\)
• E. \(15\)

Answer 1

The Correct Option is B

Concept: To find distinct prime factors:

• Express the number as product of primes
• Count unique prime numbers only

Step 1: Prime factorization of 9900.
\[ 9900 = 99 \times 100 \] \[ 99 = 9 \times 11 = 3^2 \times 11 \] \[ 100 = 10^2 = (2 \times 5)^2 = 2^2 \times 5^2 \]
Step 2: Combine factors.
\[ 9900 = 2^2 \times 3^2 \times 5^2 \times 11 \]
Step 3: Count distinct primes.
Distinct prime factors: \[ 2, 3, 5, 11 \] \[ \text{Total} = 4 \]
Step 4: Option analysis.

• (A) 7: Incorrect $\times$
• (B) 4: Correct \checkmark
• (C) 11: Not count of primes $\times$
• (D) 5: Over-counted $\times$
• (E) 15: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (B).