Primary 4 · Number & Algebra
P4 factors and multiples
A factor divides a number exactly, and a multiple is what you reach counting up in it. In P4, your child lists factors in pairs, finds common factors and common multiples, and decides which one a word problem wants.
- Taught in
- Term 1
- Syllabus
- 4 skills
- Usual slip
- Takes a common multiple
What your child learns in P4 factors and multiples
Four skills, each with what it looks like on a worksheet.
See the syllabus wording
- factors, multiples and their relationship
- determining if a 1-digit number is a factor of a given number within 100
- finding the common factors of two given numbers
- determining if a number is a multiple of a given 1-digit number
- finding the common multiples of two given 1-digit numbers
Factors and multiples go together
3 × 8 = 24, so 3 and 8 are factors of 24, and 24 is a multiple of 3 and of 8. It is one fact, read from either end.
Is it a factor? Is it a multiple?
Divide and check what is left over. 84 ÷ 7 = 12 with nothing left, so 7 is a factor of 84 and 84 is a multiple of 7. 86 ÷ 7 leaves 2.
| Division | Left over | So |
|---|---|---|
| 84 ÷ 7 = 12 | 0 | 7 is a factor of 84 |
| 86 ÷ 7 = 12 R 2 | 2 | 7 is not a factor of 86 |
Common factors
List factors in pairs, starting from 1 × the number, so none is missed. A common factor is in both lists. For 24 and 32, the common factors are 1, 2, 4 and 8.
| Factor pairs of 24 | Factor pairs of 32 |
|---|---|
| 1 × 24 | 1 × 32 |
| 2 × 12 | 2 × 16 |
| 3 × 8 | 4 × 8 |
| 4 × 6 |
Common multiples
List a few multiples of each number side by side and look for the ones in both. For 6 and 8, the first common multiple is 24, not 6 × 8 = 48.
| Multiples of 6 | Multiples of 8 |
|---|---|
| 6 | 8 |
| 12 | 16 |
| 18 | 24 |
| 24 | 32 |
| 30 | 40 |
| 36 | 48 |
Key facts and formulas
- Factors come in pairsList them in pairs, starting from 1 × the number, so none is missed.
- Is it a factor?Divide. Nothing left over means it is a factor, and the number is a multiple of it.
Left over Is 7 a factor? 91 ÷ 7 0 yes 94 ÷ 7 3 no - Common factorsList the factors of both numbers. The ones in both lists are common factors.
Factors 20 1, 2, 4, 5, 10, 20 30 1, 2, 3, 5, 6, 10, 15, 30 Both 1, 2, 5, 10 - Common multiplesList the multiples of each number. The ones in both lists are common multiples.
Multiples 4 4, 8, 12, 16, 20, 24 6 6, 12, 18, 24, 30, 36 Both 12, 24
Words to know
- Factor
- A number that divides another exactly, with nothing left over. 6 is a factor of 24.
- Multiple
- A number times 1, 2, 3 and so on. 24 is a multiple of 6.
- Factor pair
- Two factors that multiply to give the number, such as 4 × 6 for 24.
- Common factor
- A factor of both numbers. 4 is a common factor of 24 and 32.
- HCF and LCM
- Highest common factor and lowest common multiple, the names tuition books and secondary school use.
The sentence that costs the mark
Two ribbons are 12 cm and 18 cm long. Each is cut into equal pieces, as long as possible. How long is each piece?
What the working usually does
a common multiple of12 and 18=36 cm
Finds a number that is a multiple of both 12 and 18. That answers a different question: when two lengths line up.
What the question asked
the biggest common factor of12 and 18=6 cm
Finds the biggest number that divides both 12 and 18 exactly. That is the longest equal piece.
Both are real numbers worked out from 12 and 18, and a child who can find both may still pick the wrong one. A sense-check settles it: a piece cut from a 12 cm ribbon cannot be 36 cm long.
The same P4 factors and multiples question, worked properly
Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.
Nadia puts 30 pens and 45 erasers into gift bags, the same number of each in every bag, none left over. How many bags at most?
- Each bag gets the same number of pens and of erasers, with none left over. So the number of bags must divide 30 and 45 exactly. It is a common factor, not a common multiple.
- List the factor pairs of 30 in order: 1 × 30, 2 × 15, 3 × 10 and 5 × 6.
- Now the factor pairs of 45: 1 × 45, 3 × 15 and 5 × 9.
- The factors in both lists are 1, 3, 5 and 15. The biggest is 15, so each bag gets 30 ÷ 15 = 2 pens and 45 ÷ 15 = 3 erasers.
- So Nadia can make at most 15 gift bags.
Every question in StudyLah comes with a walkthrough like this one.
Try it freeThree quick P4 factors and multiples questions
Try them together, then tap to check.
Question 1
Every 4th commuter at an MRT station receives a free flyer. Every 6th commuter receives a free sticker. Find the first commuter who receives both.
Show answer
Answer12th. Flyers go to the 4th, 8th and 12th, stickers to the 6th and 12th. It is not 4 × 6 = 24.
Question 2
Which numbers are factors of both 12 and 20? List all of them.
Show answer
Answer1, 2 and 4. The factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 20 are 1, 2, 4, 5, 10 and 20.
Question 3
1, 7, 9 and 63 are some of the factors of 63. Write the other two factors.
Show answer
Answer3 and 21. The factor pairs of 63 are 1 × 63, 3 × 21 and 7 × 9.
Helping at home
How to tell it has clicked
Ask your child whether the question shares things into equal groups (a factor) or waits for two things to line up (a multiple). If they can say which, the listing takes care of itself.
A quick check catches most slips. A common factor is never bigger than the numbers. A common multiple is never smaller.
Try this tonight
Ask two questions with numbers close together. 12 sweets and 18 biscuits go into bags, the same in each, none left over: at most how many bags? Then: two buses leave every 6 and 9 minutes. When do they next leave together?
The first answer is 6 bags, a common factor. The second is 18 minutes, a common multiple. Talk about why one question splits and the other waits.
Before and after P4 factors and multiples
Builds on
Primary 3 Multiplication and DivisionMultiplies and divides, and reads the remainder
You are here
Primary 4 Factors and Multiples
Lists factors in pairs and finds multiples
The methods your child will use here
More in Primary 4
Struggling with the working rather than the topic itself? How to help your child with problem sums
See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.