The number of divisors of 9600 including 1 an | 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 (4 	imes 25) = (2^5 \

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$48$

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(C) To find the number of divisors of $9600$,we first find its prime factorization.$9600 = 96 	imes 100 = (32 	imes 3) 	imes (4 	imes 25) = (2^5 	imes 3) 	imes (2^2 	imes 5^2) = 2^7 	imes 3^1 	imes 5^2$.If a number $N$ is expressed as $N = p_1^{a} 	imes p_2^{b} 	imes p_3^{c}$,then the total number of divisors is given by $(a + 1)(b + 1)(c + 1)$.Here,$a = 7$,$b = 1$,and $c = 2$.Therefore,the number of divisors $= (7 + 1)(1 + 1)(2 + 1) = 8 	imes 2 	imes 3 = 48$.

The number of divisors of $9600$ including $1$ and $9600$ are

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