Question

The number of proper divisors of 1800 which are also divisible by 10, is

• A. 18
• B. 34
• C. 27
• D. none of these

Answer 1

The correct option is D none of these

$1800=2^3\times 3^2\times 5^2$
$=10(2^2\times 3^2\times 5^1$)
The number of proper divisors of 1800 which are also divisible by 10 are given by the factors of the numbers which is inside the parenthesis
$\therefore$ number of factors divisible by $10=(2+1)(2+1)(1+1)=18$
But one of the above factors is 1800 which is not a proper divisor
So, The number of proper divisors of 1800 which are also divisible by $10=17$
i.e. D.none of these