Finding divisor of 1080.

[jaysinhp]

Question : "Find the number of divisor of 1080 excluding the throughout divisors, which are perfect squares."

What I have done : I found the divisors of 1080 which is : 2x2x2x3x3x3x5 = 2^3 x 3^3 X 5

Let me be frank I understood that by excluding the perfect squares means I have to not count the 2^2 and so as 3^2. So I counted for total number of divisors is 2^0 x 2^1 x 3^0 x 3^1 x 5^0 x 5^1 =Considering powers (1+1) x (1+1) x (1+1) = 8 but answer is something different. I know I am mistaking in considering perfect square. Please clear my confusion so that I will able to count clearly. Thank you.

 

[pka]

Question : "Find the number of divisor of 1080 excluding the throughout divisors, which are perfect squares."

What I have done : I found the divisors of 1080 which is : 2x2x2x3x3x3x5 = 2^3 x 3^3 X 5

Have a look at this.

(3+1)(3+1)(1+1)=32 so there are thirty two divisors.

 

[jaysinhp]

Have a look at this.

(3+1)(3+1)(1+1)=32 so there are thirty two divisors.

I know there are how many devisors. What I want to know is how to count devisors excluding perfect squares. Thank you.

 

[pka]

I know there are how many devisors. What I want to know is how to count devisors excluding perfect squares. Thank you.

\(\displaystyle 1080=2^3\cdot 3^3\cdot 5\) so the squares are \(\displaystyle 1,~2^2,~ 3^2,~\&~2^2\cdot 3^2\).