What Is A Composite Number? Definition, List And Examples
The short version
- A composite number is a whole number greater than 1 that has more than two factors. In other words, something besides 1 and itself divides into it evenly.
- The first composite numbers are 4, 6, 8, 9, 10, 12, 14 and 15. The smallest is 4.
- 1 is neither prime nor composite. 2 is prime, and it’s the only even number that isn’t composite.
- To test a number, try dividing by the primes 2, 3, 5 and 7. For any number from 11 to 100, if none of those divide it evenly, it’s prime.
- There are 74 composite numbers from 1 to 100. The full list is below.
A composite number is a whole number bigger than 1 that can be made by multiplying two smaller whole numbers. 12 is composite because 12 = 3 × 4. Its factors are 1, 2, 3, 4, 6 and 12, which is more than two. Compare that with 7, which only has the factors 1 and 7, so 7 is prime.
Every whole number greater than 1 is either prime or composite, with no overlap. Below we cover how to tell the two apart quickly, a full list of composite numbers up to 100, prime factorization, the mistakes kids make most, and practice problems with answers.
What is a composite number? The definition in plain words
A factor is a number that divides into another number with no remainder. Every whole number greater than 1 has at least two factors: 1 and itself. If that’s all it has, it’s prime. If it has at least one more, it’s composite.
A handy way to picture it: try to arrange that many tiles into a rectangle with at least two rows and two columns. 12 tiles can make a 3 by 4 rectangle, so 12 is composite. 7 tiles only fit in a single row of 7, so 7 is prime.
| Number | Factors | How many factors | Type |
|---|---|---|---|
| 1 | 1 | 1 | Neither |
| 2 | 1, 2 | 2 | Prime |
| 9 | 1, 3, 9 | 3 | Composite |
| 13 | 1, 13 | 2 | Prime |
| 15 | 1, 3, 5, 15 | 4 | Composite |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 | 8 | Composite |
How to tell if a number is composite
You only need to find one factor other than 1 and the number itself. These checks find one fast:
- Even? Any even number bigger than 2 is composite, since 2 divides it.
- Digits add to a multiple of 3? Then 3 divides it. For 51, 5 + 1 = 6, so 51 = 3 × 17. Composite.
- Ends in 0 or 5? Then 5 divides it. Anything past 5 that ends this way is composite.
- Still not sure? Try 7, then 11, then 13, and so on through the primes.
When can you stop checking?
You only have to test primes up to the square root of the number. If a number has a factor bigger than its square root, it also has a partner factor smaller than it, which you’d already have found.
Is 91 prime or composite?
It’s odd, so 2 doesn’t work.
9 + 1 = 10, not a multiple of 3.
It doesn’t end in 0 or 5.
Try 7: 91 ÷ 7 = 13. It divides evenly.
91 = 7 × 13, so 91 is composite.
Is 97 prime or composite?
The square root of 97 is a bit less than 10, so test 2, 3, 5 and 7.
97 is odd. 9 + 7 = 16, not a multiple of 3. It doesn’t end in 0 or 5. 97 ÷ 7 = 13 remainder 6.
No factor found, so 97 is prime.
91 is the classic trick question. It looks prime, and a lot of adults would guess prime too.
List of composite numbers from 1 to 100
There are 74 composite numbers up to 100. The other 26 numbers are the 25 primes plus the number 1.
| Range | Composite numbers | Count |
|---|---|---|
| 1 to 10 | 4, 6, 8, 9, 10 | 5 |
| 11 to 20 | 12, 14, 15, 16, 18, 20 | 6 |
| 21 to 30 | 21, 22, 24, 25, 26, 27, 28, 30 | 8 |
| 31 to 40 | 32, 33, 34, 35, 36, 38, 39, 40 | 8 |
| 41 to 50 | 42, 44, 45, 46, 48, 49, 50 | 7 |
| 51 to 60 | 51, 52, 54, 55, 56, 57, 58, 60 | 8 |
| 61 to 70 | 62, 63, 64, 65, 66, 68, 69, 70 | 8 |
| 71 to 80 | 72, 74, 75, 76, 77, 78, 80 | 7 |
| 81 to 90 | 81, 82, 84, 85, 86, 87, 88, 90 | 8 |
| 91 to 100 | 91, 92, 93, 94, 95, 96, 98, 99, 100 | 9 |
Watch the odd ones in that list: 9, 15, 21, 25, 27, 33, 35, 39, 49, 51, 57, 63, 69, 77, 81, 87, 91 and more. Odd composite numbers are the ones kids most often mislabel as prime. The smallest odd composite number is 9.
Composite numbers and prime factorization
Every composite number can be broken down into a product of primes, and there’s only one way to do it (ignoring order). That breakdown is called its prime factorization. The usual tool is a factor tree: split the number into any two factors, then keep splitting until every branch ends in a prime.
Prime factorization of 60
60 = 6 × 10
6 = 2 × 3 and 10 = 2 × 5
60 = 2 × 2 × 3 × 5 = 22 × 3 × 5
Prime factorization of 84
84 = 4 × 21
4 = 2 × 2 and 21 = 3 × 7
84 = 22 × 3 × 7
You can start the tree with any pair of factors. 60 = 2 × 30 or 60 = 5 × 12 lead to the same primes in the end. Prime factorization is how kids later find greatest common factors, least common multiples and common denominators, so this is where composite numbers start to matter.
Common mistakes with composite numbers
- Calling 1 prime or composite. It has only one factor, so it’s neither.
- Calling 2 composite because it’s even. Its only factors are 1 and 2, so it’s prime.
- Assuming every odd number is prime. 9, 15, 21, 27, 51, 57 and 91 are all odd and composite.
- Stopping too early. Checking 2, 3 and 5 isn’t enough for 49 or 91. Both need 7.
- Mixing up factors and multiples. Factors of 12 are the numbers that go into 12 (1, 2, 3, 4, 6, 12). Multiples of 12 are what you get counting by 12s (12, 24, 36…).
Practice problems
- Is 15 prime or composite?
- Is 23 prime or composite?
- Is 1 prime or composite?
- List all the factors of 18. Is 18 composite?
- Is 51 prime or composite?
- Is 91 prime or composite?
- List the composite numbers between 20 and 30.
- Write the prime factorization of 72.
Answers
- Composite. 15 = 3 × 5.
- Prime. Its only factors are 1 and 23.
- Neither. 1 has only one factor.
- 1, 2, 3, 6, 9, 18. That’s six factors, so yes, composite.
- Composite. 5 + 1 = 6, so 3 divides it: 51 = 3 × 17.
- Composite. 91 = 7 × 13.
- 21, 22, 24, 25, 26, 27, 28. (23 and 29 are prime.)
- 72 = 8 × 9 = 2 × 2 × 2 × 3 × 3 = 23 × 32
If your child is stuck on prime and composite numbers
Sorting numbers into prime and composite is really a test of multiplication and division facts. A child who knows 7 × 13 = 91, or who can quickly check whether 3 goes into 57, finds this topic easy. A child who’s still counting on fingers for 6 × 7 has to guess, and guessing on this topic means a lot of wrong answers.
So if composite numbers aren’t sticking, check the multiplication facts first, then division with remainders. Those are core skills for grades 3 to 5, as laid out in Math Skills By Grade Level: What Your Child Should Know. Facts get solid through short, frequent practice more than long sessions, which is the argument we make in Why 20 Minutes A Day Beats A 90-Minute Tutoring Session. If you’re seeing shaky facts across the board, Is My Child Behind In Math? 12 Signs By Grade Level will help you gauge how far back the gap goes.
Frequently asked questions
What’s the meaning of a composite number?
A composite number is a whole number greater than 1 with at least one factor besides 1 and itself. 4, 6, 8, 9 and 10 are the first five.
Is 1 a composite number?
No. 1 has only one factor, itself. It’s neither prime nor composite.
What is the smallest composite number?
4. Its factors are 1, 2 and 4. The numbers 2 and 3 are prime, and 1 is neither.
Are all even numbers composite?
All except 2. Every even number greater than 2 has 2 as a factor, on top of 1 and itself.
Is 0 a composite number?
No. Prime and composite are defined only for whole numbers greater than 1, so 0 isn’t either one.
What’s the difference between prime and composite numbers?
A prime number has exactly two factors: 1 and itself. A composite number has more than two. 11 is prime; 12 is composite.
Find the actual gap
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