January 3rd, 2016, 03:07 PM  #1 
Newbie Joined: Jan 2016 From: Croatia Posts: 2 Thanks: 0  Need help
The number of all even divisers of some natural number is 3 more than the number of all odd divisers.What is the ratio of the sum of all the evennumbered divisors and the sum of all its odd divisors? Find all possibly answers.

January 3rd, 2016, 04:43 PM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
This is a good problem! Let $n$ be the number we're looking at. Write a general prime factorisation of $n$ (What prime factor do you know $n$ has?). Write out the number of odd divisors of $n$ using the prime factorisation. Write out the number of even divisors of $n$ using the prime factorisation. How do they relate? After that, there's a little bit of casework and the answer falls out. 