INTEGER FACTORIZATION

Of all the problems in the theory of numbers to which computers have been applied, probably none has been influenced more than of factoring.

We will focus on Integer Factorization in today's section.

A "Prime Number" is a whole number, greater than 1, that can be evenly divided only by 1 or itself. "Factors" are the numbers you multiply together to get another number.

"Prime Factorization" is finding which prime numbers you need to multiply together to get the original number.

Integer Factorization is the process of determining which prime numbers divide a given positive integer. Integer factorization or prime factorization is the breaking down of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer.

By the fundamental theorem of Algebra, every positive integer has a unique prime factorization. It is interesting to know that integer factorization is related to many other number theoretic problems, that is, if we can find the algorithm for integer factorization, then with some modifications, this algorithm can always be used for some other problems, such as the discrete Logarithms, square root problems, etc..