The number of positive divisors of 1080 is | vedclass

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

Question

(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

$32$

Vedclass · Answer

(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

Similar Questions

If $n$ is a factor of $72$,such that $xy = n$,then the number of ordered pairs $(x, y)$ is: (where $x, y \in N$)

If $33!$ is divisible by $2^n$,where $n \in N$,then the sum of all possible values of $n$ is:

The coefficient of $x^3 y^4 z^5$ in the expansion of $(x y+y z+x z)^6$ is

The number $111...1$ ($91$ times) is

The sum of the divisors of $2^5 \times 3^4 \times 5^2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module