What Is a Factor in Math?

In mathematics, a factor is a number or algebraic expression that divides another number or expression evenly-meaning without leaving a remainder.

Key Points:

• If a and b are numbers, and a divides b exactly, then a is a factor of b.
• For example, 3 is a factor of 12 because 12 ÷ 3 = 4 with no remainder.
• Factors come in pairs. For 12, the factor pairs are (1, 12), (2, 6), and (3, 4).
• Factors can be positive or negative since a negative times a negative also gives a positive product.

In algebra:

• Factors are expressions multiplied together to get another expression.
• For example, in the expression x2−5x+6x^2-5x+6x2−5x+6, the factors are (x−2)(x-2)(x−2) and (x−3)(x-3)(x−3) because:

(x−2)(x−3)=x2−5x+6(x-2)(x-3)=x^2-5x+6(x−2)(x−3)=x2−5x+6

Summary:

• A factor is a number or expression that divides another exactly.
• Factors help in simplifying expressions, finding divisors, and solving equations.

If you'd like, I can provide examples or explain how to find factors!