Q118 / 180 · KCET 2007 · Mathematics

The number of positive divisors of 252 is

  • A
    9
  • B
    5
  • Correct answer
    C
    18
  • D
    10

Solution

We know that, if $a=p_{1}^{\alpha_{1}} \cdot p_{2}^{\alpha_{2}} \ldots$ Then, the total number of positive divisors of $a$ is $T(a)=\left(\alpha_{1}+1\right)\left(\alpha_{2}+1\right) \ldots \ldots .$ Given, $\quad 252=2^{2} \times 3^{2} \times 7^{1}$ Here, $\quad \alpha_{1}=2, \alpha_{2}=2, \alpha_{3}=1$ $\therefore \quad T(a)=(2+1)(2+1)(1+1)$ $=3 \cdot 3 \cdot 2$ $=18$

Hence, the correct answer is option: 'C'.

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