The number of positive divisors of 252 is | vedclass

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Question

(C) We know that,if $a = p_{1}^{\alpha_{1}} \cdot p_{2}^{\alpha_{2}} \cdot p_{3}^{\alpha_{3}} \dots$ Then,the total number of positive divisors of $a$

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(C) We know that,if $a = p_{1}^{\alpha_{1}} \cdot p_{2}^{\alpha_{2}} \cdot p_{3}^{\alpha_{3}} \dots$ Then,the total number of positive divisors of $a$ is given by $T(a) = (\alpha_{1} + 1)(\alpha_{2} + 1)(\alpha_{3} + 1) \dots$ Given,$252 = 2^{2} 	imes 3^{2} 	imes 7^{1}$ Here,$\alpha_{1} = 2, \alpha_{2} = 2, \alpha_{3} = 1$ $	herefore T(252) = (2 + 1)(2 + 1)(1 + 1)$ $= 3 \cdot 3 \cdot 2$ $= 18$

The number of positive divisors of $252$ is

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