I think I'm doing this correctly but I wanted to check. I'm trying to find the torsion coefficients - sometimes called the invariant factors - of the group Z/9 * Z/14 * Z/6 * Z/8.
I start by finding the elementary divisors of each number by breaking them up into prime powers - i.e., I separate each number into its divisors until i have either prime numbers or a number that is a power of a prime.
This gives me 9, 2, 7, 2, 3, and 8 as the elementary divisors, which I then group by prime bases to get 2,2,8, 3,9, and 7.
To finish, I multiply together the largest number of each group, then second-largest in each groups, etc., until all the numbers are used. This gives me 504, 6, and 2 as my torsion coefficients