Question

The number of positive divisors of $252$ is

• A. 9
• B. 5
• C. 18
• D. 10

Answer 1

Answer: (C)

We know that, if $a=p_1^{{\alpha }_1}\cdot p_2^{{\alpha }_2}$
Then, the total number of positive divisors of $a$ is
$T(a)=\left({\alpha }_1+1\right)\left({\alpha }_2+1\right)\dots$
Given, $252=2^2\times 3^2\times 7^1$
Here, ${\alpha }_1=2,{\alpha }_2=2,{\alpha }_3=1$
$\therefore T(a)=(2+1)(2+1)(2+1)$
$=3\cdot 3\cdot 2$
$=18$