Glaisher's Factor Tables

Abstract

THERE is no general method of ascertaining whether one number is divisible, without remainder, by another specified number (less than its half) except by actual trial, or by the knowledge, otherwise acquired, of all the divisors of the first number. If then the second is not among these, it is also known that it is not a divisor of the first number. The knowledge of whether a specified number has any divisors at all, and if so what they are, is only to be obtained in general by trying it with all possible divisors less than its square root. The process can be shortened, but only to a limited extent, and, speaking generally, it would require hundreds of division sums, to ascertain by trial that 3,979,769 had 1979 for a divisor, and was consequently the product of 1979 and 2011.

Factor Table for the Fourth Million.

By James Glaisher (London: Taylor and Francis, 1880.)