Question

The number of prime factors of ${(3\times 5)}^{12}{(2\times 7)}^{10}{\left(10\right)}^{25}$ is

• A. $47$
• B. $60$
• C. $72$
• D. $94$

Answer 1

Answer: (D)

$94$

In this number, $3,5,7$ and $2$ are prime numbers.

$10$ is composite. So we factorize $10$ to get all prime factors.

$10=2\times 5$.

The number can now be written as $3^{12}\times 7^{10}\times 2^{35}\times 5^{37}$.

Since all the factors are now prime, we simply add their powers to get the

number of prime factors $=$ $12+10+35+37=94$