Good Learning Co.
SavannahYear 8
← Maths
MathsNumber sense26 min★★ difficulty

Primes, factors, multiples, HCF and LCM

Prime numbers are the atoms of arithmetic — every other whole number is built by multiplying them together.

Part of your national curriculum
  • Number: Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor and lowest common multiple

Lesson overview

What you'll learn in this lesson

Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor and lowest common multiple

Key learning points

  • • Primes and factors
  • • Worked example: HCF
  • • Worked example: LCM

This lesson at a glance

  • 26 minutes
  • 14 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

conceptsvocabularynumbersfactorsmultiples

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%
1

Watch & discover

Part 1 of 14

Watch first

Primes, factors, multiples, HCF and LCM

An English teaching video on this topic from MathTalk. Watch it, then scroll down for the lesson.

In a nutshell

Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor and lowest common multiple

2

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · Primes and factors

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 14

Learn

Primes and factors

A prime number has exactly two factors: 1 and itself, like 2, 3, 5, 7, 11. Factors of 12 are 1, 2, 3, 4, 6, 12 — numbers that divide it exactly.

4

Explore the idea

Part 4 of 14

Learn

Worked example: HCF

Find the HCF of 18 and 24. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The highest common factor is 6.

5

Quick check

Part 5 of 14

Quick check

Which of these is a prime number?

6

Reset break

Part 6 of 14

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
7

Quick check

Part 7 of 14

Quick check

What is the HCF of 18 and 24?

8

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Worked example: LCM

A short piece of teaching, then a check to make sure it has landed.

9

Explore the idea

Part 9 of 14

Learn

Worked example: LCM

Find the LCM of 4 and 6. Multiples of 4: 4, 8, 12, 16. Multiples of 6: 6, 12, 18. The lowest common multiple is 12.

10

Quick check

Part 10 of 14

Quick check

What is the LCM of 4 and 6?

11

Challenge round

Part 11 of 14

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

12

Challenge round

Part 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

A prime number has exactly two ____: 1 and itself, like 2, 3, 5, 7, 11.

Factors of 12 are 1, 2, 3, 4, 6, 12 — ____ that divide it exactly.

____ of 4: 4, 8, 12, 16.

13

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Primes, factors, multiples, HCF and LCM

4 questions, marked with the reasoning shown. No timer.

  1. 1. What is the highest common factor of 36 and 48?

  2. 2. Which of these is a prime number?

  3. 3. What is the HCF of 18 and 24?

  4. 4. What is the LCM of 4 and 6?

14

Lesson round-up

Part 14 of 14

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 14 · Watch & discover

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    Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor and lowest common multiple

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