Question

The number of positive divisors of $1512$ excluding unity and itself is

• A. 32
• B. 31
• C. 30
• D. 48

Answer 1

The correct option is C 30

$1512=2^3{3}^3{7}^1$
The positive divisor of the number can be any of the following combination of the expansion:
$(2^0+2^1+2^2+2^3)(3^0+3^1+3^2+3^3)(7^0+7^1)$
But we have to exclude unity and the number itself.
Hence, total no. of such divisors are
$\left(\begin{array}{c}4\\ 1\end{array}\right)\left(\begin{array}{c}4\\ 1\end{array}\right)\left(\begin{array}{c}2\\ 1\end{array}\right)-2=30$