Greatest Common Factor (GCF) (Grade 6)
The greatest common factor of two numbers is the largest number that divides both. To find it, list the factors of each number and pick the biggest one they share — or use prime factorization and multiply the primes they have in common. The GCF is the key to simplifying fractions and splitting things into equal groups.
Understanding greatest common factor
The greatest common factor of two numbers is the largest number that divides both. To find it, list the factors of each number and pick the biggest one they share — or use prime factorization and multiply the primes they have in common. The GCF is the key to simplifying fractions and splitting things into equal groups.
Key Idea
The greatest common factor of two numbers is the largest number that divides both. To find it, list the factors of each number and pick the biggest one they share — or use prime factorization and multiply the primes they have in common. The GCF is the key to simplifying fractions and splitting things into equal groups.
Seeing it in action
Worked example
Find the GCF of 12 and 18.
Factors of 12: 1,2,3,4,6,12. Factors of 18: 1,2,3,6,9,18.
Common factors: 1, 2, 3, 6. The greatest is 6.
The greatest shared factor is 6.
Try a few
GCF of 8 and 12
GCF of 9 and 15
GCF of 20 and 30
Factor Fields
A calm number-theory game for factors, multiples, primes, GCF, and LCM.
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Put the reasoning on paper.
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