Singapore Math factors and multiples guide for families and teachers outside Singapore: what Primary 4 students learn, the exact syllabus limits, and how to practise at home.
Factors and multiples are two views of the same multiplication fact.
In 3 × 8 = 24, 3 and 8 are factors of 24, and 24 is a multiple of both.
In Singapore Mathematics, factors and multiples are a Primary 4 topic. Students test whether a 1-digit number is a factor of a number within 100, find common factors of two numbers, and find common multiples of two 1-digit numbers.
The ideas return in fractions and ratio. In Secondary 1, they grow into prime factorisation, HCF and LCM.
This guide is useful for families and teachers who want to:
- know exactly what Primary 4 includes;
- teach factors and multiples in a clear sequence;
- prepare a child who is moving into a Singapore school; or
- support a student using Singapore Math materials in another country.
Quick facts
Level: Primary 4 (common to all students); revisited in Primary 5 Foundation Mathematics
Strand: Number and Algebra
Official source: MOE Primary Mathematics Syllabus, the 2021 syllabus first examined at PSLE in 2026
Comes after: Multiplication Tables and Multiplication and Division
Leads to: Ratio and Prime Factorisation, HCF and LCM
What Factors and Multiples Mean in Singapore Mathematics
A factor of a number divides it exactly, with no remainder. 4 is a factor of 24 because 24 ÷ 4 = 6.
A multiple of a number is the result of multiplying it by a whole number. 24 is a multiple of 4 because 4 × 6 = 24.
So the two ideas are linked: 4 is a factor of 24 exactly when 24 is a multiple of 4.
Factors come in pairs. The factor pairs of 24 are 1 and 24, 2 and 12, 3 and 8, and 4 and 6.
A number has only a few factors, but it has endless multiples: 4, 8, 12, 16 and so on, without stopping.
Where Factors and Multiples Sit in the Singapore Syllabus
At Primary 4, students learn:
- factors, multiples and the relationship between them;
- to test whether a 1-digit number is a factor of a number within 100;
- to find the common factors of two numbers;
- to test whether a number is a multiple of a 1-digit number; and
- to find the common multiples of two 1-digit numbers.
Primary 5 Foundation Mathematics revisits the same factors and multiples content as Primary 4 Standard.
| Level | How factors and multiples are used |
|---|---|
| Primary 4 | Factors, multiples, common factors and common multiples, within the limits above |
| Primary 4 | Adding and subtracting fractions with different denominators, where common multiples help |
| Primary 6 | Writing ratios in simplest form, which uses common factors |
| Secondary 1 | Primes and prime factorisation; HCF and LCM; squares, cubes, square roots and cube roots by prime factorisation |
The Primary 4 list does not name prime numbers, HCF or LCM. Those appear by name in the Secondary 1 content.
How Singapore Teaches Factors and Multiples
1. Build rectangles
Arrange 12 counters into as many rectangles as possible: 1 by 12, 2 by 6 and 3 by 4. Each side length is a factor of 12.
2. Find factor pairs in order
Start at 1 and work upward: 1 × 24, 2 × 12, 3 × 8, 4 × 6. Stop when the pairs begin to repeat.
3. Link multiples to the tables
The multiples of 6 begin with the table of 6: 6, 12, 18, 24 and onwards. Secure tables make this topic much easier.
4. Test with division
To test whether 7 is a factor of 84, divide. 84 ÷ 7 = 12 with no remainder, so it is.
5. Compare two lists
Common factors appear in both lists of factors. Common multiples appear in both lists of multiples.
6. Use them in later topics
Common factors help to simplify fractions and ratios. Common multiples help to add fractions with different denominators.
Worked Examples
Common factors
Question: Find the common factors of 24 and 36.
Step 1. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Step 2. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 3. The numbers in both lists are 1, 2, 3, 4, 6 and 12.
Check: 24 ÷ 12 = 2 and 36 ÷ 12 = 3, with no remainders.
The greatest of these, 12, is the one that later simplifies 24/36 to 2/3 in one step.
Common multiples
Question: Pencils come in packs of 4 and erasers in packs of 6. What is the smallest number of pencils and erasers you can buy so that you have the same number of each?
Step 1. Multiples of 4: 4, 8, 12, 16, 20, 24, and so on.
Step 2. Multiples of 6: 6, 12, 18, 24, and so on.
Step 3. The first number in both lists is 12.
Step 4. Buy 12 pencils (3 packs) and 12 erasers (2 packs).
Check: 3 × 4 = 12 and 2 × 6 = 12.
Common Mistakes
- Mixing up factors and multiples. The child lists 8, 12 and 16 as factors of 4. Fix: factors divide into the number; multiples come out of its table.
- Missing a factor pair. The child lists the factors of 36 but leaves out 4 and 9. Fix: test 1, 2, 3, 4 and onwards in order, and record each pair.
- Forgetting 1 and the number itself. Every number from 2 upwards has at least these two factors. Fix: write 1 and the number first, then fill in between.
- Thinking multiples stop. The child says 24 is “the last multiple” of 4. Fix: show that the list continues: 28, 32, 36 and so on.
- Assuming the product is the smallest common multiple. For 4 and 6, the child gives 24. Fix: list multiples of both and look for the first match, which is 12.
Teaching Factors and Multiples Outside Singapore
- HCF and LCM. Singapore says “highest common factor” (HCF). Some curricula call it the greatest common factor (GCF) or greatest common divisor (GCD). LCM is common to both. In the syllabus, HCF and LCM are named in Secondary 1.
- Primes. The Primary 4 list does not name prime numbers. Primes and prime factorisation are listed in the Secondary 1 content.
- Limits. Primary 4 tests 1-digit factors of numbers within 100, and common multiples of two 1-digit numbers. Keep early practice within these limits.
- Timing. Use the Singapore Math Grade Levels guide rather than converting ages.
- Prerequisites. This topic depends on the tables of 2 to 10 and on division with remainder. Repair those first if they are weak.
How to Practise Factors and Multiples at Home
- Build rectangles from a pile of counters and name the factor pairs.
- List the factors of one number between 12 and 60 each day.
- Answer one “Is 7 a factor of …?” question by dividing.
- Write the first ten multiples of a 1-digit number.
- Find the common multiples of two 1-digit numbers by comparing lists.
- Once a week, use a common factor to simplify a fraction.
Ten minutes a day is enough when it is regular.
Try These
- Is 7 a factor of 91?
- Is 84 a multiple of 6?
- Find the common factors of 18 and 30.
- Find the first three common multiples of 6 and 8.
Answers
- Yes. 91 ÷ 7 = 13, with no remainder.
- Yes. 6 × 14 = 84.
- 1, 2, 3 and 6. The factors of 18 are 1, 2, 3, 6, 9 and 18. The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
- 24, 48 and 72. These are the first three numbers that appear in both lists of multiples.
What Comes Next
- Adding and Subtracting Fractions uses common multiples to find a shared denominator.
- Ratio in Primary 6 uses common factors to write ratios in simplest form.
- Prime Factorisation, HCF and LCM in Secondary 1 gives a faster method for larger numbers.
A child who finds factor pairs quickly is well prepared for all three.
Frequently Asked Questions
When do Singapore students learn factors and multiples?
In Primary 4, where the content is common to all students. Primary 5 Foundation Mathematics revisits the same content.
Are prime numbers part of Primary 4?
The Primary 4 list does not name them. Primes and prime factorisation appear in Secondary 1.
Do Primary 4 students learn HCF and LCM?
They find common factors of two numbers and common multiples of two 1-digit numbers. The terms HCF and LCM are named in Secondary 1.
How large are the numbers?
Students test whether a 1-digit number is a factor of a number within 100. Common multiples are found for two 1-digit numbers.
Is 1 a factor of every number?
Yes. 1 divides every whole number exactly. For example, the factors of 7 are 1 and 7.
Why do factors matter later?
They are used to simplify fractions and ratios. In Secondary 1 they lead to prime factorisation, HCF and LCM, and later to factorisation in algebra.
Helpful Reading
- Singapore Mathematics | International Edition: Multiplication and Division
- Singapore Mathematics | International Edition: Ratio
- Singapore Mathematics | International Edition: Prime Factorisation, HCF and LCM
- Primary Mathematics: Factors, Multiples and Divisibility | Worked Learning Guide
- How the Secondary 1 Factors to Algebra Interface Works
- MOE Primary Mathematics Syllabus
- SEAB PSLE Mathematics Syllabus 0008
Factors and Multiples in Singapore Mathematics
Factors divide in.
Multiples come out.
Find the pairs in order.
Compare two lists to see what they share.
Keep within 100 at first.
These small ideas sit under fractions, ratio and secondary algebra.
Taught carefully in Primary 4, they make all three easier.
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Singapore Mathematics | International Edition is a Bukit Timah Tutor guide series for families and teachers outside Singapore. It is not a textbook and is not affiliated with MOE, SEAB or any publisher. Syllabus details were checked against MOE and SEAB documents in October 2026. Always confirm current requirements with your school.
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