Greatest Common Divisor 3.4.3 47.

So far as the resultant velocity ratio is concerned, the order of the drivers N and of the followers n is immaterial: but to secure equable wear of the teeth, as explained in 44, the wheels ought to be so arranged that, for each elementary combination, the greatest common divisor of N and ii shall be either 1, or as small as possible.

They there fore study that the numbers of teeth in each pair of wheels whici work together shall either be prime to each other, or shall hav their greatest common divisor as small as is consistent with velocity ratio suited for the purposes of the machine.

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If we resolve two numbers into their prime factors, we can find their Greatest Common Divisor or Highest Common Factor (written G.C.D.