Greatest Common Factor (GCF) (Grade 6)
The greatest common factor of two numbers is the largest number that divides both.
Understanding greatest common factor
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.
A common mistake, and the fix
Picking a common factor that isn’t the greatest, or finding a common multiple instead.
2 and 3 both divide 12 and 18, but the greatest common factor is 6. The GCF can’t be bigger than the smaller number; an answer such as 36 is a common multiple of 12 and 18, not a factor.
Try a few
GCF of 8 and 12
factors of 8: 1, 2, 4, 8; of 12: 1, 2, 3, 4, 6, 12.
GCF of 9 and 15
factors of 9: 1, 3, 9; of 15: 1, 3, 5, 15.
GCF of 20 and 30
20 = 10 × 2 and 30 = 10 × 3.
Factor Fields
A calm number-theory game for factors, multiples, primes, GCF, and LCM.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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