(ii.) To continue the division we may take as our new unit a submultiple of Q, such as Q/r, where r is an integer, and repeat the process.
Submultiples.-The relation of a unit to its successive multiples as shown in a multiple-table is expressed by saying that it is a submultiple of the multiples, the successive submultiples being one-half, one-third, one-fourth,..
The relation of submultiple is the converse of that of multiple; thus if a is I of b, then b is 5 times a.
The determination of a submultiple is therefore equivalent to completion of the diagram E or E' of § 35 by entry of the unit, when the number of times it is taken, and the product, are given.
Dividing 12 by 2, we get a submultiple 6, which again has a prime 2 as a factor.