For (a), construct a surjective (onto) homomorphism from to whose kernel is , then apply the First Isomorphism Theorem for groups.

For (b), recall that 'modding' out by H just means we impose the relation (10m+4n,12m+4n)=(0,0) in . In which subgroup of does 10m+4n=0 for all m,n? 12m+4n=0? The product of these two groups is what you are looking for.

For (c), look at gcd(a,b) and gcd(c,d), and recall that the gcd(x,y) can always be written as a linear combination of x and y.