Number System Practice Test 1

$6^5\times 7^6\times {11}^{10}$ $=2^5\times 3^5\times 7^6\times {11}^{10}$
The total number of divisors of $\mathit{N}={\mathit{a}}^{\mathit{p}}\times {\mathit{b}}^{\mathit{q}}\times {\mathit{c}}^{\mathit{r}}\times {\mathit{d}}^{\mathit{s}}$.
where all a, b, c and d are prime numbers is given by (p + 1) (q + 1) (r + 1) (s + 1)
So, total number of divisors
= (5 + 1) (5 + 1) (6 + 1) (10 + 1) = 6 × 6 × 7 × 11
= 2,772.