Question

The number of even proper divisors of 1008 is

• A. $24$
• B. $23$
• C. $22$
• D. none of these

Answer 1

The correct option is B $23$

$1008=2^4\times 3^2\times 7$
= $2(2^3\times 3^2\times 7)$
by multiplying every divisor of the number within the brackets, we can find the even divisors of the given number as every number with in the brackets will be multiplied by 2 which is taken out and gives the even divisors
$\therefore$ number of even divisors $=(3+1)(2+1)(1+1)$
$=24$
but the above divisors also contain the 1008 which is not a proper divisor
$\therefore$ number of proper divisors $=23$