Question

The number of divisors of 9600 including 1 and 9600 are

• A. 60
• B. 58
• C. 48
• D. 46

Answer 1

The correct option is C 48

Method For an integer $N>1$

$N=p^a\times q^b\times r^c\times .....$

where $p,q,r,....$ are prime factors of $N$

and $a,b,c,...$ are prime factors $p,q,r...$ respective;y.

Then, No, of divisor of $N=(a+1)(b+1)(c+1)....$

In equation, $9600=2^7\times 3^1\times 5^2$

Here, $A=7,b=1,c=2$

$\therefore$ No. of divisor of $9600$ are

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

$=8\times 2\times 3=48$