There are several cases in which the factors of a number may be of use in ordinary mathematical processes; as for example, in the calculation of logarithms. This, although not the raison d’être of such a table, is so important an application as to deserve special notice, for by its means the number of numbers whose logarithms are known is greatly extended. For example, Abraham Sharp’s table contains 61-decimal Briggian logarithms of primes to 1,100, so that the logarithms of all numbers whose greatest prime factor does not exceed this number, may be obtained by simple addition. Similarly, Wolfram’s table gives 48-decimal hyperbolic logarithms of primes up to 10,009. Thus a factor table forms a very valuable complement to many-place logarithmic tables, the range of which must necessarily be comparatively limited ; and even in the case of large prime numbers, or numbers exceeding the limits of the factor table, it affords a very convenient method of calculating logarithms.