Factors and Multiples
Factors, common factors, multiples, common multiples and prime numbers, and how to tell them apart.
⏱ 7 min · 🎯 5 things to master
Have you ever shared a packet of 12 sweets and wondered which group sizes split evenly? You can give 2 friends 6 each, or 3 friends 4 each, or 4 friends 3 each — but 5 friends will not work. The numbers that divide evenly are called factors, and they are everywhere in maths. Once you understand factors and multiples, fractions, ratio and tricky number puzzles all become easier. Let's meet them.
Parents: let your child predict before they reveal each step. The blue dotted words are tappable definitions, and the "Method tip" boxes name exactly what a PSLE marker rewards in the working — not just the final number.
By the end you'll be able to list factors, find common factors, list multiples, find common multiples, and spot a prime number. Let's begin.
Factors
A of a number divides into it with nothing left over. To find all the factors of 12, hunt in pairs: 1 × 12, 2 × 6, 3 × 4. So the factors of 12 are 1, 2, 3, 4, 6 and 12. Working in pairs means you never miss one.
Every number has 1 and itself as factors. Listing them in order, smallest to largest, keeps you tidy and shows the marker you found them all.
🤔 Predict first: Which list shows ALL the factors of 18?
Common factors
When two numbers share a factor, it is a . List the factors of each number, then find the ones in both lists. The factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 18 are 1, 2, 3, 6, 9, 18. The numbers in both are 1, 2, 3 and 6 — those are the common factors.
This is exactly how you simplify a fraction later: you divide top and bottom by a common factor.
🤔 Predict first: What are the common factors of 8 and 12?
Multiples
A of a number is what you get from its times table. The multiples of 4 are 4, 8, 12, 16, 20, and on forever. Unlike factors, there is no end to the list of multiples — you can always go one step further.
A quick way to think about it: a multiple of 4 can always be divided by 4 with no remainder. So 28 is a multiple of 4 because 28 ÷ 4 = 7, but 30 is not.
🤔 Predict first: Which number is a multiple of 6?
Common multiples
When two numbers share a multiple, it is a . List the multiples of each and find ones in both. Multiples of 3 are 3, 6, 9, 12, 15, 18. Multiples of 4 are 4, 8, 12, 16, 20, 24. The first one in both is 12 — the smallest common multiple.
This is how you add unlike fractions: you find a common multiple of the denominators to make the bottoms match.
🤔 Predict first: What is the smallest common multiple of 4 and 6?
Prime numbers
A has only two factors — 1 and itself. So 7 is prime because nothing else divides it, but 9 is not prime because 3 divides it. The primes start 2, 3, 5, 7, 11, 13. Notice that 2 is the only even prime — every other even number can be divided by 2.
A common trap: 1 is not prime, because it has only one factor (itself), not two.
🤔 Predict first: Which of these is a prime number?
Watch out — these are easily mixed up
Quick recap
🎯 Mastery check
Answer all 6 — your progress is saved on this device.
Which list gives all the factors of 20?
What is the largest common factor of 16 and 24?
Which number is a multiple of 7?
What is the smallest common multiple of 6 and 8?
Which of these is a prime number?
A teacher wants groups that split both 24 girls and 36 boys evenly. Which group size works?