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[[[>50 Remember, an integer is a number with no fractional part, and might be positive, negative, or zero. However, when we talk about integer factorisation it suffices to restrict ourselves to positive numbers. ]]] Integer factorisation is the problem of finding a non-trivial divisor of a given number. A factor of $n$ is a number that divides $n,$ and non-trivial means neither 1 nor $n.$ For example, a non-trivial factor of 11111 is 41, whereas trivial factors are 1, -1, 11111 and -11111. If /n/ is a prime number then by definition it has no non-trivial factors. There are techniques for identifying non-primes that do not explicitly exhibit a factor, so the question of finding a non-trivial divisor is interesting. The RSA public key cryptosystem uses numbers that are hard to factor, and if a way could be found to factor numbers quickly then that would effectively break it. * http://www.google.co.uk/search?q=Factoring+Integers