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  4. The number of positive divisors of 252 is

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Q. The number of positive divisors of $252$ is

KCETKCET 2007Binomial Theorem

Solution:

We know that, if $a = p_1^{\alpha_1} . p_2^{\alpha 2} ...$
Then, the total number of positive divisors of a
is $T (a) = (\alpha_1 + 1) (\alpha_2 + 1 )......$
Given, $252 = 2^2 \times 3^2 \times 7^1$
Here, $\alpha_1 = 2, \alpha_2 = 2, \alpha_3 = 1$
$\therefore \; T (a) = (2 + 1) (2 + 1) (1 + 1)$
$= 3 . 3 . 2$
$= 18$