Question

Number of even proper divisors of $196$ is

• A. $5$
• B. $10$
• C. $15$
• D. $20$

Answer 1

Answer: (A)

$5$

$N=p^m{q}^n$ where N is composite number and $p$ and $q$ are prime numbers
Then, Total factors of $N$ $=(m+1)(n+1)$

$196=2^2\times 7^2$
Total factors of $196=(2+1)(2+1)=9$
clearly odd divisors of $196$ are$1,7,49$
$\therefore \text{number of even divisors of 196 = 9 - 3 = 6}$
but one number 196 is also a divisor of itself,
and 196 is not a proper divisor of itself.
$\therefore \text{Total number of even proper divisors of 196 = 6 - 1 = 5}$