Greatest common factor
from class:
College Algebra
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.
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5 Must Know Facts For Your Next Test
- The GCF of two numbers can be found using the Euclidean algorithm.
- When factoring polynomials, the GCF should be factored out first.
- The GCF is helpful in simplifying rational expressions by reducing both numerator and denominator by their GCF.
- Finding the GCF is essential when solving problems involving least common multiples (LCM).
- 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?
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