Primary 4 Factors and Multiples Study Guide
Primary 4 factors and multiples in four short steps: factor ladders, shared factors, lined-up lists of multiples, and packing and repeating stories. Each step has something to tap, and worked examples come after.
Start here
What are factors and multiples?
A factor divides a number exactly. A multiple is what you reach by counting on in equal steps.
3 × 4 = 12, so 3 and 4 are factors of 12, and 12 is a multiple of 3 and of 4. A number has only a few factors, and they come in pairs. Its multiples go on for ever. When two numbers share a factor or a multiple, it is called common.
In this chapter, your child learns to:
- find the factors of a number in pairs, starting at 1;
- test whether a 1-digit number is a factor of a number up to 100;
- find the common factors of two numbers, and the greatest one;
- list multiples and find common multiples of two 1-digit numbers;
- decide whether a word problem needs a common factor or a common multiple.
Step 1
Finding factors with factor pairs
Start at 1 and look for pairs in order. A factor pair multiplies to make the number exactly. Test 1, then 2, then 3, and so on. If a number leaves a remainder, it is not a factor. Stop when the pairs turn round: every factor is now on the ladder, and each one is written only once.
Tap Next step
Which number is a factor of 76?
Step 2
Common factors of two numbers
A common factor must appear on both ladders. Write the full ladder for each number first. Then read both numbers in every pair and ring the ones that stand on both ladders. The greatest of them is the greatest common factor: the biggest number that divides both exactly.
Tap a number on both ladders
What is the greatest common factor of 18 and 30?
Step 3
Multiples and common multiples
Line up the two lists and look for a match. The multiples of 6 are 6, 12, 18 and so on: count on in sixes. Write the multiples of each number in order, from the smallest upwards. A number on both lists is a common multiple. The first match is the first common multiple, and every later match is a multiple of it.
Which number between 50 and 70 is a common multiple of 4 and 6?
Step 4
Factors and multiples in word problems
Read what the question asks: the number of items, or the number of packs. Sharing a fixed amount into equal groups with none left over needs a common factor, often the greatest one. When things repeat, or two pack sizes must give the same total, list the multiples and find a common multiple. Then read the question again: it may want the items or the packs.
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Drag, or tap + and −
Cups are sold in packs of 4 and plates in packs of 6. Mrs Tan buys an equal number of cups and plates. What is the smallest number of packs of plates she can buy?
Primary 4 factors and multiples questions, worked step by stepCover the working and try each one on paper. Then open the hint, or reveal one line at a time.
List all the factors of 45.
- 45 = 1 × 45
- = 3 × 15. 2 and 4 leave a remainder.
- = 5 × 9. 6, 7 and 8 leave a remainder, and 9 × 5 is the same pair turned round.
- The factors of 45 are 1, 3, 5, 9, 15 and 45.
Find the first two common multiples of 8 and 12.
- Multiples of 8: 8, 16, (24), 32, 40, (48)
- Multiples of 12: 12, (24), 36, (48)
- 24 = 3 × 8 = 2 × 12, and 48 = 6 × 8 = 4 × 12.
- The first two common multiples are 24 and 48.
(a) List the common factors of 36 and 48. (b) What is the greatest common factor of 36 and 48?
- 36 = 1 × 36 = 2 × 18 = 3 × 12 = 4 × 9 = 6 × 6
- 48 = 1 × 48 = 2 × 24 = 3 × 16 = 4 × 12 = 6 × 8
- (a) The common factors are 1, 2, 3, 4, 6 and 12.
- (b) The greatest common factor is 12.
Ali goes to the library every 4 days. Ben goes every 6 days. Both of them are at the library on 1 March. On what date will they next be at the library on the same day?
- Multiples of 4: 4, 8, (12), ...
- Multiples of 6: 6, (12), ...
- They are next there together 12 days after 1 March.
- 1 + 12 = 13, so the date is 13 March.
Mr Lee has 32 pencils and 40 erasers. He packs all of them into bags. Every bag has the same number of pencils and the same number of erasers, with none left over. (a) What is the greatest number of bags he can pack? (b) How many erasers are in each bag?
- 32 = 1 × 32 = 2 × 16 = 4 × 8
- 40 = 1 × 40 = 2 × 20 = 4 × 10 = 5 × 8
- Common factors: 1, 2, 4, 8. (a) The greatest number of bags is 8.
- (b) 40 ÷ 8 = 5 erasers in each bag.
Step 5
Check yourself
Five quick questions to finish. Nothing is saved, and each answer leads to the practice that fits it.
1. Which number is not a factor of 60?
2. What is the greatest common factor of 24 and 40?
3. Which of these is a multiple of 7?
4. What is the first common multiple of 6 and 9?
5. Bus A leaves every 10 minutes and Bus B every 15 minutes. Both leave together at 08 00. When do they next leave together?
How to use this guide. Sit with your child for Step 1 and say each test aloud: does 3 go into 28 exactly? Keep a pencil nearby so each ladder and each list goes on paper too, in the same order as on screen. One step takes about five minutes.
When a word problem comes up, ask two things before any working. Is something being shared out, or repeated until it matches? And does the question want the items or the packs? The worked examples run in this order, from one ladder to two-part packing stories.
More study guides
P4 Factors and Multiples lessons and practice
3 lesson videos and 40 questions across three subtopics, from Basic to Challenge, each with a worked solution.
Watch and practise →