Factoring IntegersYou are currently
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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.
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