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.

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