ISI2016-DCG-20

Question

The total number of factors of $3528$ greater than $1$ but less than $3528$ is

• A. $35$
• B. $36$
• C. $34$
• D. None of these

Answer 1

Answer: $\mathbf{C}$

The total number of factors is given by:

$\mathrm {N= (a+1)(b+1)(c+1)}$ where $\mathbf a$, $\mathbf b$, and $\mathbf c$ are the powers of the prime factors.

So, $3528$ can be written as $2^33^27^2$

$\Rightarrow \mathrm { a = 3, b =2, c = 2}$

 $=\mathrm {(a+1)(b+1)(c+1) = 4.3.3 = 36}$

But we have to remove the factors $1$ and $3528$ (as given in the question)

$\therefore$ Total number of factors $=36-2 = 34$

$\therefore \mathbf C $ is the correct option.