DeepMaths / Fun Maths

Fun Maths Book 2 Online Learning Programme

For Year 4 and Year 5

Chapter 3: Multiplication, Division, Factors, and Multiples

Multiplication, Division, Factors and Multiples

Use arrays and written methods to multiply and divide, then break numbers into prime factors.

Fun Maths Book 2 pages 32-515 minutes

AI teacher

Press Start to hear a short classroom-style explanation. If sound is unavailable, the full script is shown below.

Voice: Browser voice

Workbook pages

Fun Maths Book 2 pages 32-51

Practise written multiplication, division, factors, multiples, HCF, LCM and prime factor trees.

AI explanation

The AI teacher links multiplication to arrays, division to equal sharing and grouping, and factors to numbers that multiply together. Prime factor trees are introduced as a neat way to keep splitting until every branch ends in a prime number.

  1. 1Multiplication can be seen as equal rows and columns.
  2. 2Division asks how many equal groups or how many in each group.
  3. 3Factors are numbers that multiply to make another number.
  4. 4In a prime factor tree, keep splitting composite numbers until every leaf is prime.

Think with the AI teacher

Today we will connect multiplication, division, factors and multiples. They are not separate tricks; they are one family of ideas.

Question 1

Pause 4s

If 6 x 7 = 42, what does that tell us about 42?

After thinking

It tells us that 6 and 7 are factors of 42, and 42 is a multiple of 6 and 7.

Fantastic connection. One fact can tell us several things.

Question 2

Pause 5s

When we split 84 in a factor tree, when should we stop splitting?

After thinking

We stop when every branch ends in a prime number.

Yes. Prime leaves are the final building blocks.

Question 3

Pause 4s

How are multiplication and division connected?

After thinking

They undo each other and describe equal groups from different directions.

Great thinking. That connection helps with checking.

Deep structure

What children discover

Children discover that factors, multiples, division facts and arrays are different views of the same structure.

Common mistake

Children may confuse factors with multiples, for example calling 36 a factor of 9 instead of a multiple.

Future connection

Factors and multiples prepare students for fractions, HCF, LCM, ratio, algebraic factorisation and prime factor methods.

FractionsHCF and LCMRatioAlgebraic factorisation

Animated demonstration

See the maths move

An array rearranges into equal groups, then a number grows a factor tree whose branches finish with highlighted prime leaves.

Arrays reveal equal groups, grouped counters connect to division, and the factor tree shows composite numbers breaking into prime building blocks.
84127342 x 2 x 3 x 7

Guided examples

Two-digit multiplication

Find 34 x 26.

  1. 1.Break 26 into 20 + 6.
  2. 2.34 x 20 = 680.
  3. 3.34 x 6 = 204.
  4. 4.Add the two partial products.
Answer: 884

Prime factor tree

Write 84 as a product of prime factors.

  1. 1.Split 84 into 12 x 7.
  2. 2.7 is prime.
  3. 3.Split 12 into 3 x 4.
  4. 4.3 is prime. Split 4 into 2 x 2.
Answer: 84 = 2 x 2 x 3 x 7

Interactive practice

Try it now

For one workbook number, list factor pairs first, then decide whether it is prime or composite.

0/3 correct

Which number is a factor of 36?

Which is a multiple of 7?

Which list contains only prime numbers?

Review

Explain the difference between a factor and a multiple before starting workbook pages 32-51.

Explain the difference between a factor and a multiple using the number 36.

Parent signal

A child who knows tables but struggles with HCF or LCM may need more factor-list practice.

You are seeing the structure inside numbers. That is strong maths thinking.