Question

Let $d\left(n\right)$ denote the number of divisors of $n$ including $1$ and itself. Then $d\left(225\right)$, $d\left(1125\right)$ and $d\left(640\right)$ are

• A. in AP
• B. in HP
• C. in GP
• D. consecutive integers

Answer 1

The correct option is C in GP

$225=3^2\times 5^2$
$d\left(225\right)=3\times 3=9$

$1125=3^2\times 5^3$
$d\left(1125\right)=3\times 4=12$

$640=2^7\times 5^1$
$d\left(640\right)=8\times 2=16$

Since, ${12}^2=9\times 16$
$\therefore 9,12,16$ are in GP