factorization

Factorization is the process of breaking a number or an algebraic expression into factors, which are smaller parts that multiply together to make the original whole. It is mainly a mathematical idea, and you will see it often in arithmetic, algebra, and computer science.

In arithmetic, it means finding ways to write a number as a product of smaller numbers. For example, 36 can be written as $2 \times 18$, $3 \times 12$, $4 \times 9$, or $6 \times 6$. Often, people are especially interested in prime factorization, where a number is broken into prime numbers only. So 12 becomes $2 \times 2 \times 3$.

In algebra, factorization means rewriting an expression as a product of simpler expressions. For example, $x^{2} + 5x + 6$ can be written as $(x + 2)(x + 3)$. This helps when solving equations, simplifying expressions, or seeing how different parts of an expression are connected.

The idea is also important in computer science, especially in cryptography. Some security systems depend on the fact that very large numbers are hard to break into their prime factors. Because of that, the word can appear in both school math and technical writing.

At its heart, factorization is about taking something written as one whole and showing the multiplied parts inside it. Once you can see those parts clearly, many math problems become easier to understand and solve.