Question

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

Answer 1

Answer:

Step-by-step explanation:

Ok since no one decided to answer my question, here is the answer

from aops:

We note that

$5400 = 2^3 3^3 5^2 . The square-free divisors of this number therefore have the form 2^a 3^b 5^c where each of a , b , c is zero or a one. The sum of all such integers is\[ (1+2)(1+3)(1+5). \](The proof of this fact is analogous to our proof for the formula for the sum of the divisors of a positive integer.) Therefore our answer is 3 \cdot 4 \cdot 6 = \boxed{72} .$

as you can see, the "verified answer" is complete garbage.

Answer 2

Consider the positive squares of 1,2,3,4, 5, ...
They are 1, 4, 9, 16, 25, ...

Factorize 5400 with regard to these positive squares.
5400 = 4 * 1350
          = 4 * 9 * 150
          = 4 * 9 * 25 * 6

The positive square free divisors of 5400 are 4,9 and 25.
Their sum is  4+9+25 = 38

Answer: 38