In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. Factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, 3 × 5 is a factorization of the integer 15 and is a factorization of the polynomial x² – 4 factors as (x − 2) (x + 2). In all cases, a product of simpler objects is obtained. It is the opposite of expansion.
The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra.
It can be used for many things, like helping perform arithmetic operations. Now we group the factors so that it is easier for us to multiply. Another way to use factorization is to find the least common multiple and greatest common factors.