Here is a question that trips up students at every level. Is 6 a factor or a multiple of 12? If you had to think about it for more than a second, this guide is for you. The difference between factor and multiple sounds simple but the two words get swapped constantly — in homework, in tests, and even by students who know their times tables perfectly. The good news is that once the distinction clicks, it genuinely never gets confused again.
A factor is a number that divides exactly into another number without leaving a remainder. Factors are smaller than or equal to the number. A multiple is a number you get by multiplying a number by any whole number. Multiples are larger than or equal to the original number. Factors go into a number. Multiples come out of a number.
Difference Between Factor and Multiple: Comparison Table
| Feature | Factor | Multiple |
|---|---|---|
| Definition | A number that divides exactly into another | A number produced by multiplying a number by a whole number |
| Size | Always smaller than or equal to the number | Always larger than or equal to the number |
| How many are there? | A finite number of factors | Infinite multiples |
| Operation used | Division (divides in exactly) | Multiplication (multiply to get them) |
| Example for 6 | 1, 2, 3, 6 are all factors of 6 | 6, 12, 18, 24, 30… are multiples of 6 |
| Does it include the number itself? | Yes, every number is a factor of itself | Yes, every number is a multiple of itself |
| Key question | What divides into this number? | What do I get when I multiply this number? |
What is a Factor?
A factor of a number is any whole number that divides into it exactly, leaving no remainder. Think of factors as the numbers that fit neatly inside another number when you divide.
To find all the factors of a number, you go through the whole numbers one by one and check which ones divide in exactly. The easiest method is to work in pairs.
Example: Find all the factors of 12
1 x 12 = 12, so 1 and 12 are factors
2 x 6 = 12, so 2 and 6 are factors
3 x 4 = 12, so 3 and 4 are factors
5 does not divide into 12 exactly, so 5 is not a factor
The factors of 12 are: 1, 2, 3, 4, 6, 12
Important things to remember about factors:
- 1 is always a factor of every number
- Every number is a factor of itself
- Factors are always less than or equal to the number
- Every number has a finite (limited) number of factors
- Prime numbers have exactly two factors: 1 and themselves
What is a Multiple?
A multiple of a number is what you get when you multiply that number by any whole number (1, 2, 3, 4, 5 and so on). Multiples are essentially the numbers in that number’s times table.
Example: Find the first six multiples of 4
4 x 1 = 4
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24
The first six multiples of 4 are: 4, 8, 12, 16, 20, 24
Important things to remember about multiples:
- Every number is a multiple of itself (4 x 1 = 4)
- Multiples are always greater than or equal to the original number
- Every number has infinitely many multiples — they never end
- Multiples of even numbers are always even
- You can check if a number is a multiple by dividing — if it divides exactly, it is a multiple
Example 1 – Sharing sweets equally (Factors):
You have 24 sweets and want to share them equally among friends with none left over. The number of friends you can share with must be a factor of 24. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. So you could share with 2, 3, 4, 6, 8, or 12 friends and have no sweets left over. You could not share equally with 5 friends because 5 is not a factor of 24.
Example 2 – Bus timetables (Multiples):
A bus comes every 8 minutes starting from minute 0. The times the bus arrives are multiples of 8: 8, 16, 24, 32, 40, 48 minutes and so on. This is a real-world use of multiples — any repeating event at regular intervals produces a sequence of multiples.
Example 3 – Arranging chairs in rows (Factors):
A teacher needs to arrange 30 chairs into equal rows with no chairs left over. The number of chairs per row must be a factor of 30. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The teacher could make 5 rows of 6, 6 rows of 5, or 3 rows of 10 — all because these are factor pairs of 30.
Example 4 – Times tables (Multiples):
Every times table is a list of multiples. The 7 times table gives you the multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70. Any number in the 7 times table is a multiple of 7. This is why knowing your times tables makes multiple questions very quick to answer.
Example 5 – Finding common ground (HCF and LCM):
The Highest Common Factor (HCF) of two numbers is the largest factor they share. The Lowest Common Multiple (LCM) is the smallest multiple they share. For 12 and 18: the HCF is 6 (the largest number that divides into both) and the LCM is 36 (the smallest number that both 12 and 18 divide into). HCF uses factors. LCM uses multiples.
The family trick:
Factors are like Family — they are smaller and they came before the number. They are what make up the number when multiplied together.
Multiples are like More — they are always equal to or more than the number. You get them by going further along the times table.
Or try this: Factor = Fits inside (divides in). Multiple = Makes bigger (multiplies up). Factors fit inside. Multiples make bigger numbers.
Quick Quiz: Factor or Multiple?
1. Is 4 a factor or a multiple of 20?
2. Is 35 a factor or a multiple of 7?
3. Which of these is a factor of 18: 6 or 24?
4. Which of these is a multiple of 9: 3 or 45?
5. How many factors does the number 7 have?
Difference Between Factor and Multiple in Exams
The difference between factor and multiple is tested in maths exams from Year 4 all the way through to GCSE. Questions include listing all factors of a number, finding multiples up to a given value, identifying whether a number is a factor or multiple of another, and finding the Highest Common Factor (HCF) or Lowest Common Multiple (LCM) of two numbers. Always read the question carefully to check whether it is asking for factors or multiples — the two words are used precisely in exam questions and mixing them up costs easy marks.
Common Mistakes to Avoid
Confusing which is bigger:
Factors are always smaller than or equal to the number. Multiples are always larger than or equal to the number. If someone asks for a factor of 10 and you write 20, that is wrong because 20 is larger than 10. Factors fit inside. Multiples grow outward.
Forgetting 1 and the number itself:
Every number has at least two factors: 1 and the number itself. Students often forget to include 1 when listing factors. For example, the factors of 9 are 1, 3, and 9 — not just 3 and 9.
Thinking multiples end somewhere:
Multiples go on forever. There is no last multiple of any number. The multiples of 5 are 5, 10, 15, 20… and they continue infinitely. Exam questions usually ask for the first few multiples, but remember the list never actually ends.
Mixing up HCF and LCM:
HCF (Highest Common Factor) uses factors. LCM (Lowest Common Multiple) uses multiples. Students frequently use the wrong method for each. Remember: H for Highest, H for factors sharing (going down). L for Lowest, L for multiples sharing (going up).
Frequently Asked Questions
Can a number be both a factor and a multiple of another number?
Yes. Every number is both a factor and a multiple of itself. For example, 6 is a factor of 6 (because 6 divides into 6 exactly once) and 6 is also a multiple of 6 (because 6 x 1 = 6). This is the one case where a number sits in both categories at the same time.
What is the difference between HCF and LCM?
HCF stands for Highest Common Factor. It is the largest number that divides exactly into two or more numbers. LCM stands for Lowest Common Multiple. It is the smallest number that two or more numbers both divide into exactly. HCF involves finding shared factors. LCM involves finding shared multiples. For 12 and 18, the HCF is 6 and the LCM is 36.
Is 1 a factor of every number?
Yes. 1 divides exactly into every whole number, so 1 is a factor of every number. Similarly, every number is a multiple of 1 (because any number multiplied by 1 equals itself). This is why 1 always appears in every factor list.
What are prime factors?
Prime factors are the factors of a number that are also prime numbers. Every whole number greater than 1 can be written as a product of its prime factors. For example, the prime factors of 12 are 2 and 3, because 12 = 2 x 2 x 3. Finding prime factors is called prime factorisation and it is a key skill for finding HCF and LCM efficiently.
How do I quickly check if one number is a multiple of another?
Divide the larger number by the smaller number. If the result is a whole number with no remainder, then the larger number is a multiple of the smaller one. For example, is 84 a multiple of 7? 84 divided by 7 equals 12 exactly, so yes, 84 is a multiple of 7. If there is a remainder, it is not a multiple.
For more Maths help visit Khan Academy: Factors and Multiples.
Also read: Difference Between Mean, Median and Mode | Difference Between Perimeter and Area | Difference Between Permutation and Combination
The difference between factor and multiple is really about direction. Factors go into a number. Multiples come out of a number. Once that distinction is clear in your head, the difference between factor and multiple becomes one of the easiest topics in maths to get right every time. Keep practising with different numbers and the difference between factor and multiple will feel completely automatic before your next exam.
The difference between factor and multiple is one of those topics that rewards practice more than memorisation. Try picking any number and listing all its factors and first ten multiples. Do that with a few different numbers and the difference between factor and multiple will stop feeling like a definition you have to remember and start feeling like something you simply know. That is when the difference between factor and multiple truly clicks.