Question

Find the number of divisors of 10800

• A. 57
• B. 60
• C. 72
• D. None of These

Answer 1

The correct option is B 60

$10800=3\times 3\times 3\times 2\times 2\times 2\times 2\times 5\times 5$
$10800=3^3\times 2^4\times 5^2$
$n=a^p,b^q,c^r$
Than the number of divisors $n=(p+1)\times (q+1)\times (r+1)$
$Heren=10800,a=3,b=2,c=5,p=3,q=4,c=2$
$\Rightarrow n=(3+1)\times (4+1)\times (2+1)$
$\Rightarrow n=4\times 5\times 3=60$