Question

The number of divisors a number $38808$ can have, excluding $1$ and the number itself is

• A. $70$
• B. $72$
• C. $71$
• D. none of these

Answer 1

Answer: (A)

$70$

When we write a number $N$ in terms of its prime factor, then number of divisor can be by formula,

$(a+1)(b+1)(c+1)(d+1)..$

$N=P^a{Q}^b{R}^c{S}^d..$

For $38808=2^3{3}^2{7}^{2}11$

Total number of divisor are given by $(3+1)(2+1)(2+1)(1+1)$.

Now we have been asked to remove $1$ and $70$, so subtract two from the above value and we get $70$ divisors