What is the Factoring Problem?

Factoring is the act of splitting an integer into a set of smaller integers (factors) which, when multiplied together, form the original integer. For example, the factors of 15 are 3 and 5; the factoring problem is to find 3 and 5 when given 15. Prime factorization requires splitting an integer into factors that are prime numbers; every integer has a unique prime factorization. Multiplying two prime integers together is easy, but as far as we know, factoring the product is much more difficult.