Case 1. If n is a divisor of N,
a = N; b = N/n; c = 1.
(20)
Case 2. If the greatest common divisor of N and n be d, a number less than n, so that n = md, N = Md; then
a = mN = Mn = Mmd; b = M; c = m.
(21)
Case 3. If N and n be prime to each other,
a = nN; b = N; c = n.
(22)
It is considered desirable by millwrights, with a view to the preservation of the uniformity of shape of the teeth of a pair of wheels, that each given tooth in one wheel should work with as many different teeth in the other wheel as possible. They therefore study that the numbers of teeth in each pair of wheels which work together shall either be prime to each other, or shall have their greatest common divisor as small as is consistent with a velocity ratio suited for the purposes of the machine.