Question

The number of distinct prime factors in the product $(30)^7 \times (22)^5 \times (34)^{10}$ is:

• A. 3
• B. 4
• C. 5
• D. 7

Hint:

Ignore powers—only count unique prime numbers.

Answer 1

The Correct Option is C

Concept: Find prime factorization and count distinct primes.
Step 1: Factorize each number.
\[ 30 = 2 \times 3 \times 5 \] \[ 22 = 2 \times 11 \] \[ 34 = 2 \times 17 \]
Step 2: List distinct primes.
\[ \{2, 3, 5, 11, 17\} \]
Step 3: Count them.
\[ {Total distinct primes} = 5 \]
Hence, the answer is 5.