What is the total number of divisors of 9600, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) To find the number of divisors of $9600$,we first find its prime factorization.$9600 = 96 	imes 100 = (32 	imes 3) 	imes (10^2) = (2^5 	imes 3

Vedclass · Accepted Answer

$48$

Vedclass · Answer

(C) To find the number of divisors of $9600$,we first find its prime factorization.$9600 = 96 	imes 100 = (32 	imes 3) 	imes (10^2) = (2^5 	imes 3^1) 	imes (2^2 	imes 5^2) = 2^7 	imes 3^1 	imes 5^2$.If a number $N$ is expressed as $p_1^{a} 	imes p_2^{b} 	imes p_3^{c}$,the total number of divisors is given by $(a+1)(b+1)(c+1)$.Here,$a=7$,$b=1$,and $c=2$.Total number of divisors = $(7+1)(1+1)(2+1) = 8 	imes 2 	imes 3 = 48$.

What is the total number of divisors of $9600$,including $1$ and $9600$?

Similar Questions

The total number of $4$-digit numbers whose greatest common divisor with $54$ is $2$ is $..........$.

Let $N = n(n+1)(n+2)(n+3)$ where $n$ is a natural number,and $d$ is the number of divisors of $N$. Which of the following is true?

The sum of all positive divisors of $242$ except $1$ and itself is:

The number of integers $q$,$1 \leq q \leq 2021$,such that $\sqrt{q}$ is rational and $\frac{1}{q}$ has a terminating decimal expansion,is

The number of divisors of $7!$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module