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 $(8+1)(5+1)(1+1)(1+1)(1+1)-2$
$=9 \times 6 \times 2 \times 2 \times 2-2=432-2=430$