Greatest Common Factor
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 12 of 58.
A common factor of two numbers divides both of them. List the factors of 18 and of 30: 18 has 1, 2, 3, 6, 9 and 18, and 30 has 1, 2, 3, 5, 6, 10, 15 and 30. The numbers on both lists, 1, 2, 3 and 6, are the common factors.
The largest of them, 6, is the greatest common factor, or GCF, of 18 and 30. It is the biggest number that divides both with nothing left over: 18 is three 6s and 30 is five 6s.
The GCF answers questions about splitting two amounts into equal groups, and later in this section it is the number that simplifies a fraction in one step. For small numbers, listing factor pairs as in Chapter 1 always finds it.
Challenge
Find the greatest common factor g of 24 and 36. List the factors of each number, find the largest one they share, write g = ... on the board, then press Check.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Factors & Fractions
1Factors and Multiples
What a Factor IsFactor PairsDivisibility RulesMultiplesPrime or CompositeRecap: Factors and Multiples4What a Fraction Is
Parts of a WholeFractions on the LineA Fraction of a NumberImproper FractionsRecap: What a Fraction Is7Multiplying Fractions
Top Times TopCancel FirstWhole Times FractionA Fraction of a FractionRecap: Multiplying Fractions10Fractions in Stories
Part of a GroupWhat Is LeftSharing a FractionScaling a RecipeRecap: Fraction Stories2Prime Factorization
Factor TreesUsing ExponentsOne Tree per NumberBigger NumbersRecap: Prime Factorization5Equivalent Fractions
Same Amount, New NameSimplifying FractionsSimplify in StepsComparing FractionsRecap: Equivalent Fractions3GCF and LCM
Greatest Common FactorGCF from Prime FactorsLeast Common MultipleLCM from Prime FactorsGCF or LCM?Recap: GCF and LCM