Find the Greatest Common Factor

Students find the greatest common factor (GCF) of two whole numbers up to 100 using lists of factors and prime factorization. They apply the GCF to factor expressions of the form a + b = GCF(a,b)(__ + __) and solve real-world problems involving grouping.

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Grade 6 · Greatest Common Factor and Least Common Multiple · question 1 of 3

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20 rungs. A star at the top.

The GCF of 4 and 6 is

How it is taught

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The GCF is the largest factor two numbers share.

It cannot be larger than the smaller number.

Read it: The greatest common factor

18 has the factors 1, 2, 3, 6, 9 and 18, and 30 has the factors 1, 2, 3, 5, 6, 10, 15 and 30. The greatest number in both lists is 6: the greatest common factor.

List each number's factors in pairs that multiply to it: 1 × 18, 2 × 9, 3 × 6.
Find the factors on both lists.
The greatest of them is the GCF.

A factor divides the number exactly, so it is never bigger than the number.

The GCF writes a sum as a product: 18 + 30 = 6 × (3 + 5), and 3 and 5 share no factor but 1.

Every common factor divides the GCF: 1, 2 and 3 all divide 6.

List the factors of both numbers; the greatest number on both lists is the GCF.

Giving a common multiple instead: 90 is a multiple of both 18 and 30.

A factor divides the number, so it is never bigger than 18: the GCF is 6.

The GCF of 14 and 35 is ___ — 7. 14 = 7 × 2 and 35 = 7 × 5, and 2 and 5 share no factor but 1.

GCF(12, 18)

Today we'll find the greatest common factor — the GCF — of twelve and eighteen. That's the biggest number that divides evenly into BOTH.

Here's the plan: list every factor of each number, then find the biggest one they share.

Factors of twelve are one, two, three, four, six, and twelve.

Factors of eighteen are one, two, three, six, nine, and eighteen.

Now we circle the numbers in BOTH lists: one, two, three, and six. These are the common factors.

Grade 6 · Find the biggest factor 12 and 18 share

Which common factor is the biggest? Six!

So the greatest common factor of twelve and eighteen is six. Nice work!

What you see

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MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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