Factors, Multiples, Prime and Composite Numbers

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 List the Factors in Your Copy
5 Class Challenge
Pupil practice

1 - Getting Started ~4 mins

Key point

Illustration for Getting Started Here is a number: 12. Which whole numbers divide evenly into 12, with nothing left over?

Put your hand up and call one out when you have it. And here is the harder part: how would we be sure we have found all of them, and not missed any?

Teacher Notes

Take four or five hands-up answers and jot each on the board as it comes — don't order them yet. Leave the "how do we know we've got them all?" question hanging; it is the thread the whole lesson pulls on. Do not reveal the pairing trick here — that lands in Watch and Notice.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~11 mins

The interactive shows four different number grids: multiples, factors and primes. Look at how the squares are shaded on each one, and be ready to say what pattern you see and why some numbers are left out.

Teacher Notes

Multiples of 6: 6, 12, 18, 24, 30, 36 and on. Trace the slant with your finger before moving on.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Say each as a pair that multiplies to 24 — 1 and 24, 2 and 12, 3 and 8, 4 and 6. Work up from 1, stop when pairs meet in the middle; this pairing answers the Getting Started question.

Primes under 20: 2, 3, 5, 7, 11, 13, 17, 19 — each has exactly two factors, itself and 1. Pause on the empty 1 and ask why. Revoice: 1 has only one factor, so it misses out.

Is 51 prime? Let them guess prime first. Point to 3 and 17: these are its factors, since 3 × 17 = 51, so 51 is composite. Stress these are the numbers that break 51, not 51 itself — heads off odd means prime.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

Key point

We work through these together on one grid, one at a time — the grid clears between each so we see one clean pattern each time: first the factors of 18, then the factors of 30, then the multiples of 4, and finally the multiples of 7. One pupil comes to the board to shade each one, and everyone else's job is to call out the factors and multiples aloud and agree or correct together. Notice how the factors sit in scattered pairs, while the multiples march along a steady step.

Factors and multiples together

Teacher Notes

This round is for talking it through together — no marking yet.

Call each number and let one pupil come up to shade while the class names the numbers aloud. Say every factor pair as a multiplication as it lands ("1 and 18, 2 and 9, 3 and 6"). Clear the grid between each shading so only one pattern shows at a time. When you switch to multiples, ask the class to name the next one before it is shaded so they are counting on, not reading off. Watch for the classic slip: shading 8 as a factor of 18 (it isn't — 18 ÷ 8 leaves a remainder).

+15 XP

4 - List the Factors in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, do this:

List the factors of 12, 18 and 24 on three rows, pairing them up as you go so you don't miss any.
Underline any factor that shows up on all three rows — those are the common factors.

We will work the common-factor step together first with these three numbers, so everyone sees how to spot and underline them, before you finish the lists in your own copy.

If you finish early, try this too:

On each row, circle the number itself (12, 18 or 24) — remember every number is a factor of itself.

Teacher Notes

Walk the room glancing at the three rows — check pupils have paired their factors so none are missing. This is whole-class copybook practice, not marking.

Worked example before they write (board): List factors of 12, 18 and 24 in three rows, saying each pair as a multiplication: 12 → 1×12, 2×6, 3×4; 18 → 1×18, 2×9, 3×6; 24 → 1×24, 2×12, 3×8, 4×6. Then scan down the columns together and underline only the numbers that appear on every row: 1, 2, 3, 6. Say why each is common (it divides all three evenly) and why 4 is not (missing from 18). Pupils then copy the three lists and the underlines into their books.

Listing the factors of all three plus underlining the common ones is the core task; the circle step is for early finishers. A common miss is leaving out the number itself (12 is a factor of 12), or underlining a factor that appears on only two rows.

+10 XP

5 - Class Challenge ~8 mins

Key point

Today's challenge bank builds up: shade all the multiples of 3, then of 4, then of 5, then of 7, then of 8, and finally of 12. Before each one, predict how the pattern will look — will the shaded cells be crowded or spread out?

Shade the multiples

Teacher Notes

These are the practice questions — pupils check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

Have the class predict the density before each shade (multiples of 3 are crowded; multiples of 12 are sparse). The multiples-of-12 round is the key one — pupils should notice its shaded cells are also multiples of 3 AND of 4, tying the whole bank together. Use the Check ✓ as part of your narration: "yes — that's every one."

+15 XP

Pupil practice

Module 2 · Operations and Computational Fluency Number

Lesson 28 · Factors, Multiples, Prime and Composite Numbers

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This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~11 mins

3 - Try It Together ~11 mins

Factors and multiples together

4 - List the Factors in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Shade the multiples

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