Greatest common factor

Definition

The greatest common factor (GCF) of two or more numbers is the largest number that divides each of them without leaving a remainder. It is useful in simplifying fractions, factoring polynomials, and solving equations.

5 Must Know Facts For Your Next Test

1. The GCF of two numbers can be found using the Euclidean algorithm.
2. When factoring polynomials, the GCF should be factored out first.
3. The GCF is helpful in simplifying rational expressions by reducing both numerator and denominator by their GCF.
4. Finding the GCF is essential when solving problems involving least common multiples (LCM).
5. If two numbers are coprime, their GCF is 1.

Review Questions

• What is the greatest common factor of 18 and 24?
• How do you use the Euclidean algorithm to find the GCF of 56 and 98?
• Why is it important to factor out the GCF first when factoring polynomials?

Related terms

Least Common Multiple (LCM): The smallest multiple that is exactly divisible by every number in a set.

Prime Factorization: Expressing a number as a product of its prime factors.

Coprime: Two numbers are coprime if their greatest common factor is 1.