Question

How to find number of divisors of a number.

Answer 1

Compute required divisors.

Write the number in this form $\mathrm{n}={\mathrm{p}}^{\mathrm{a}}{\mathrm{q}}^{\mathrm{b}}{\mathrm{r}}^c$.

$\mathrm{n}$ is the number $\mathrm{p},\mathrm{q},\mathrm{r}$ are prime numbers and $\mathrm{a},\mathrm{b}$, and $\mathrm{c}$ are the powers.

The number of divisors $=(\mathrm{a}+1)(\mathrm{b}+1)(\mathrm{c}+1)$.

Example: $12=2^2\times 3^1$

Number of divisors of $12$

$$\begin{gathered} =(2+1)(1+1) \\ =3\times 2 \\ =6 \end{gathered}$$

Therefore, this is the way to find the number of divisors of a number.