A factor divides a number without leaving a remainder. The factors of 12 are 1, 2, 3, 4, 6, and 12. Every number has at least two factors: 1 and itself. Prime numbers have exactly these two.

Factoring means writing a number as a product of its factors. Prime factorization breaks it down into primes: 12 = 2² × 3. This decomposition is unique, a result known as the fundamental theorem of arithmetic.

In algebra, factoring applies to expressions. x² − 9 factors as (x − 3)(x + 3). Factoring is used to solve equations, simplify fractions, and find common denominators. In number theory, factoring large integers is computationally hard, a fact that underpins RSA encryption. The concept is simple to introduce and deep in its consequences.

• Divides a number exactly
• Prime factorization is unique
• Applies to numbers and algebraic expressions
• Hardness of integer factoring secures RSA