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

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(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

$48$

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(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 $9600$?

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