Knowing the prime number factorization of a number gives complete knowledge about all factors of that number. For instance, the above factorization of 6936 tells us that the positive factors of 6936 are of the form
Once the prime factorizations of two numbers are known, their greatest common divisor and least common multiple can be found quickly. Since determining prime number factorizations is in general a laborous process, Euclid's algorithm is in practice preferred, however.
The fundamental theorem ensures that multiplicative functions are completely determined by their values on the powers of prime numbers.