How Can You Mentally Factor Numbers Without a Calculator?

[qntty]

Does anybody have any good tricks to quickly factor a number in your head, or a trick that can be done quickly on paper? The best method that I know without using a calculator is the traditional method of finding two not-necessarily-prime factors and factoring those with the same method.

 

[ramsey2879]

Does anybody have any good tricks to quickly factor a number in your head, or a trick that can be done quickly on paper? The best method that I know without using a calculator is the traditional method of finding two not-necessarily-prime factors and factoring those with the same method.

Google "divisibility rules" or "divisibility tests" . However, mental calculations are generally restricted to working with small numbers and are not generally useful in serious number theory problems, and I don't see any advantage to excluding the use of a calculator.