Question

The number of proper divisors of the number obtained by dividing $13!$ with $100$ is

• A. 216
• B. 430
• C. 214
• D. 790

Answer 1

Answer: (B)

$13!=2\times 3\times 4\times 5\times 6\times 7\times 8\times 9\times 10\times 11\times 12\times 13$
$13!$ is divided by $100$
Then, $\frac{13!}{100}=2^8\times 3^5\times 7^1\times 11^1\times 13^1$
The number of proper divisor at the number obtained is $(8+1)(5+1)(1+1)(1+1)(1+1)-2$
$=9\times 6\times 2\times 2\times 2-2=432-2=430$