Question

$2^m{3}^n{5}^p$ is a divisor of $2^{10}{.3}^8{.5}^7$ if m,n and p are all whole numbers such that $0\le m\le 10,0\le n\le 8$ and $0\le p\le 7$. Also,
$(2^0+2^1+2^2+...+2^{10})(3^0+3^1+3^2+...+3^8)(5^0+5^1+5^2+...+5^7)$ = sum of all divisors of $2^{10}{.3}^8{.5}^7$.

The number of proper divisors of $16200$ is

• A. $60$
• B. $24$
• C. $59$
• D. $22$

Answer 1

Answer: (C)

$59$

$16200=2^3{.3}^4{.5}^2$
Thus number of proper divisor is $=(3+1)(4+1)(2+1)-1=60-1=59$
Note: A proper divisor of a positive integer is any divisor other than itself.