Greatest common factor

Definition

The greatest common factor (GCF) of two or more integers is the largest positive integer that divides each of the numbers without leaving a remainder. It is used to simplify fractions and factor polynomials.

5 Must Know Facts For Your Next Test

1. The GCF can be found using the prime factorization method, where you break down each number into its prime factors and multiply the common factors.
2. Another method to find the GCF is the Euclidean algorithm, which involves repeated division.
3. In polynomial expressions, the GCF is used to factor out the greatest common monomial from each term.
4. When solving quadratic equations, factoring out the GCF can simplify the equation and make it easier to solve.
5. The GCF is particularly useful in simplifying rational expressions by reducing them to their lowest terms.

Review Questions

• What are two methods for finding the greatest common factor?
• How does factoring out the GCF help in solving quadratic equations?
• Why is finding the GCF important when simplifying rational expressions?

Related terms

Least Common Multiple (LCM): The smallest positive integer that is divisible by each of two or more given integers.

Prime Factorization: The process of breaking down a number into its basic building blocks, which are prime numbers.

Polynomial: A mathematical expression consisting of variables, coefficients, and exponents combined using addition, subtraction, multiplication, and sometimes division.