Question

Number of even proper divisors of $240$ is

• A. $20$
• B. $19$
• C. $16$
• D. $15$

Answer 1

The correct option is D $15$

$240=2^4\times 3\times 5=2^a\times 3^b\times 5^c$
where a varies from 0 to 4 i.e. 5 divisors
b varies form 0 to 1 i.e. 2 divisors
c varies from 0 to 1 i.e. 2 divisors
Total no of divisors = $5\times 2\times 2=20$
$240=2(2^3\times 3\times 5)$
no of even divisors = $4\times 2\times 2=16$
excluding 240,
Number of even proper divisors = $15$