Number

Prime factors

Pair primes. Discover HCF and LCM.

Predict, test and explain

Step 1 of 3

Predict

What is the HCF of 18 and 24?

12=2×2×318=2×3×312=2\times2\times3\qquad 18=2\times3\times3

First number

Shared

Second number

Choose a prime on each side to pair them. Choose a shared tile to separate it.

shared product=1\text{shared product}=1

Every repeated prime needs its own tile.

InvestigateWhy does each shared prime appear only once in the overlap?

Explore and compare

Find two different numbers with this highest common factor.

HCF⁡=6\operatorname{HCF}=6

Try it in the simulation. Change one thing at a time.

Hint

Both numbers need the prime factors of six. Avoid adding another shared factor.

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Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

Use prime factors to find the highest common factor of 18 and 24.

18=2×32,24=23×318=2\times3^2,\qquad24=2^3\times3

Hint

Take each shared prime the smaller number of times.

Reveal answer

6. Both numbers contain one factor of 2 and one factor of 3.

HCF⁡(18,24)=2×3=6\operatorname{HCF}(18,24)=2\times3=6

Build an explanation

Hint 1

Match equal prime tiles from the two numbers.

Hint 2

Keep a separate tile for every repeated prime.

Hint 3

Multiply the shared primes for HCF; multiply all remaining and shared tiles once for LCM.

Worked example

This example uses fixed values, separate from the diagram controls.

Find the HCF and LCM of 12 and 18.

  1. 12 = 2 × 2 × 3; 18 = 2 × 3 × 3.
  2. Pair one 2 and one 3; their product is 6.
  3. The shared and unpaired tiles give 2 × 3 × 2 × 3 = 36.

Answer: HCF = 6; LCM = 36.

Connect this idea

Watch out: Repeated primes count separately; matching one 2 does not match every 2.