The number of positive divisors of 1080 is | vedclass

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(B) First,find the prime factorization of $1080$: $1080 = 108 	imes 10 = (12 	imes 9) 	imes (2 	imes 5) = (2^2 	imes 3^1 	imes 3^2) 	imes (2^1

Vedclass · Accepted Answer

$32$

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(B) First,find the prime factorization of $1080$: $1080 = 108 	imes 10 = (12 	imes 9) 	imes (2 	imes 5) = (2^2 	imes 3^1 	imes 3^2) 	imes (2^1 	imes 5^1) = 2^3 	imes 3^3 	imes 5^1$. If a number $N$ is expressed as $p_1^{a} 	imes p_2^{b} 	imes p_3^{c}$,then the number of positive divisors is given by $(a+1)(b+1)(c+1)$. Here,$a=3, b=3, c=1$. Number of divisors $= (3+1)(3+1)(1+1) = 4 	imes 4 	imes 2 = 32$.

The number of positive divisors of $1080$ is

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