Powers, Indices, LCM and GCF

Lessons

Primary 6 · Mathematics

Powers, Indices, LCM and GCF

6 lessons

Lesson 5 of 6

Factors and the Greatest Common Factor (GCF)

30 min

Let's begin

Umutoni has 24 avocados and 36 oranges from her family's farm. She wants to pack them into identical baskets for the market, with none left over. What is the greatest number of baskets she can make?

Factors

A factor of a number divides it exactly, with no remainder. Find factors in pairs:

36 = 1 \times 36 = 2 \times 18 = 3 \times 12 = 4 \times 9 = 6 \times 6

So the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

Common factors and the GCF

A number that is a factor of two numbers is a common factor. The biggest one is the Greatest Common Factor (GCF). (Some books call it the Highest Common Factor, HCF.)

Worked example

GCF of 18 and 24.

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 3, 6. The GCF is 6.

Using prime factors

Take only the primes that appear in every number, each with its lowest power, and multiply.

Worked example

GCF of 48 and 72.

48 = 2⁴ × 3 and 72 = 2³ × 3².
Both have 2 and 3. Lowest powers: 2³ and 3.
GCF = 2³ × 3 = 8 × 3 = 24.

Problems that need the GCF

Worked example

Umutoni's baskets.

Each basket must hold the same number of avocados and the same number of oranges, so the number of baskets must divide both 24 and 36.
The greatest number of baskets is GCF(24, 36) = 12.
Each basket gets 24 ÷ 12 = 2 avocados and 36 ÷ 12 = 3 oranges.

Worked example

Two ropes are 84 cm and 126 cm long. They must be cut into pieces that are all the same length, as long as possible, with nothing wasted.

The piece length must divide both 84 and 126: GCF(84, 126) = 42 cm.
Number of pieces: 84 ÷ 42 + 126 ÷ 42 = 2 + 3 = 5 pieces.

Words like greatest number of groups, largest possible size and share equally with none left over point to the GCF.

Tip

GCF divides; LCM multiplies up. The GCF is never bigger than the smallest of your numbers, because it has to fit into all of them.

✦

Try it yourself

Work each one in your exercise book first, then tap Show answer to check.

1

List all the factors of 30.

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Answer: 1, 2, 3, 5, 6, 10, 15, 30.

2

Find the GCF of 20 and 32.

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Answer: 4. Factors of 20: 1, 2, 4, 5, 10, 20; factors of 32: 1, 2, 4, 8, 16, 32.

3

Find the GCF of 45 and 75 using prime factors.

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Answer: 45 = 3² × 5 and 75 = 3 × 5², so GCF = 3 × 5 = 15.

4

A teacher has 40 pencils and 64 exercise books. She makes identical packs with nothing left over. What is the greatest number of packs, and what is in each?

Show answerHide answer

Answer: GCF(40, 64) = 8 packs, each with 5 pencils and 8 exercise books.

Quick check

Which list shows all the factors of 28?

What you learned today

Factors come in pairs; a common factor divides two numbers exactly.
The GCF is the greatest common factor: list factors, or multiply the shared primes with their lowest powers.
Use the GCF for “greatest number of equal groups” and “largest equal pieces” problems.

Sources and credits

Grade 6, Unit 7, Lesson 16: Common Factors, IM 6–8 Math, authored by Illustrative Mathematics and originally developed by Open Up Resources, licensed under CC BY 4.0. Adapted by Ganzaa.
Mathematics Grade 8, 1.5 Multiples and factors, Siyavula, licensed under CC BY 3.0 (licence notice read on the page, 23 September 2026). Adapted by Ganzaa.

The stories, Rwandan worked examples and practice questions were written by Ganzaa.

1Factors

2Common factors and the GCF

3Using prime factors

4Problems that need the GCF

Try it yourself

Factors

Common factors and the GCF

Using prime factors

Problems that need the GCF