\(\sc{FACTORIZATION}\) is a decision variant of the familiar problem of finding the prime factorization of a given number \(x\) – i.e. the unique sequence of primes \(p_i\) and exponents \(a_i\) such that \(x = p_1^{a_1} \cdot \ldots \cdot p_k^{a_k}\). It is not difficult to see that if there existed an efficient algorithm for deciding \(\sc{FACTORIZATION}\), then there would also exist an efficient algorithm for determining prime   factorizations.[3]   It is also easy to see that the function taking \(x\) to its prime factorization is effectively computable in the traditional sense of computability theory. For instance, it can be computed by the trial division algorithm.