Bézout's identity is essential to many applications of Euclid's algorithm, such as demonstrating the unique factorization of numbers into prime factors. To illustrate this, suppose that a number "L" can be written as a product of two factors "u" and "v", that is, "L" = "uv". If another number "w" also divides "L" but is coprime with "u", then "w" must divide "v", by the following argument: If the greatest common divisor of "u" and "w" is 1, then integers "s" and "t" can be found such that