That's not exactly true. E.g. -1 is also a "factor" of 3: -3 * -1 = 3 In number theory we define primes as a subset of the natural numbers, which excludes nega

That's not exactly true. E.g. -1 is also a "factor" of 3: -3 * -1 = 3 In number theory we define primes as a subset of the natural numbers, which excludes negative integers. But when you move on to abstract algebra, the definition of a prime element in a commutative ring is an element p, such that p|ab implies p|a or p|b. Using this definition, we can conclude that the prime elements in the ring of integers are both the positive and negative primes.