The number of divisors of 9600 including 1 and 9600 are

KCET 2020

Solution

The correct answer is 48

Explanation

$9600=2^7 \times 3 \times 5^2$

∴ Number of divisors =

$(7 + 1)(1 + 1)(2 + 1)$ =

$8 \times 2 \times 3 = 48$