Find the sum of the positive square free divisors of 5400.

Note: A natural number is square free if it is not the multiple of any perfect square greater than 1.

Question

Find the sum of the positive square free divisors of 5400.

Note: A natural number is square free if it is not the multiple of any perfect square greater than 1.

sshayer · Answer

|dw:1472005234691:dw|
now try to write required divisors

sshayer · Answer

i think only divisors are 2,3,5,6 which are not multiples of square numbers.

sshayer · Answer

10 is also there.

ganeshie8 · Answer

How about 15

sshayer · Answer

yes it is also there.
I am thinking about more if any.

sshayer · Answer

30 is also there.

sshayer · Answer

so for we are able to find 2,3,5,6,10,15,30

boynet · Answer

I think I got it now.  I figured out a formula.  The prime factorization consists of 2,3, and 5.  (2+1) * (3+1) * (5+1) = 3*4*6=72.  I think thats the answer?
Thanks for the help!

ganeshie8 · Answer

Nice, it seems we have to find the sum of all the divisors of $2\times 3\times 5$

ganeshie8 · Answer

72 looks good !

boynet · Answer

Thanks again