Composite Number in Math: Definition & Examples

Definitionnoun phrase

What is a composite number?

A composite number is a whole number greater than 1 that has more than two factors. It can be divided evenly by a number other than 1 and itself: 12 is composite because 1, 2, 3, 4, 6 and 12 all divide it. Every whole number above 1 is either prime or composite; 1 is neither.

In Spanish: número compuesto
Also called: composite, not prime
Grade level: K-5

Grade 4Grade 5Grade 6CCSS 4.OA.B.4GED

Composite Number in a picture

From 1 to 30 there are 19 composite numbers and 10 primes. Every even number after 2 is composite, but so are odd numbers such as 9, 15, 21, 25 and 27.

Formal definition and notation

A whole number n > 1 is composite if it can be written as n = a × b with whole numbers 1 < a ≤ b < n; equivalently, it has a factor other than 1 and n. A whole number greater than 1 that is not composite is a prime number. Every composite number has a prime factor no larger than √n, and it can be written as a product of primes in exactly one way, apart from order.

Symbol	Read it as	Meaning
n = a × b	n equals a times b	a factor pair; if a and b are both greater than 1, n is composite
2² × 3	two squared times three	the prime factorization of the composite number 12

Key facts

4 is the smallest composite number. The composite numbers below 20 are 4, 6, 8, 9, 10, 12, 14, 15, 16 and 18.
Every even number greater than 2 is composite, because 2 is a factor.
Every number greater than 5 that ends in 0 or 5 is composite, because 5 is a factor.
If the digits add up to a multiple of 3, the number is divisible by 3: 51 (5 + 1 = 6) is 3 × 17.
Some odd composites look prime: 9, 15, 21, 27, 33, 49, 51, 57, 87 and 91.

Composite test: find one factor pair

n is composite if n = a × b with 1 < a ≤ b < n

n: the whole number greater than 1 you are testing
a: a small factor to look for: try 2, 3, 5, 7, … up to √n
b: the matching factor, n ÷ a

One factor pair is enough. 221 is not even and its digits sum to 5, but 221 = 13 × 17, so it is composite.

Try it: test a number

Interactive

Type a whole number or press a sample. The tool lists its factors, says whether it is prime or composite, and builds its factor tree. Try 51 and 91, which look prime.

This interactive needs JavaScript. The worked examples below show the same ideas step by step.

Composite Number examples, step by step

Example 1: List the factors

Warm-up

Is 27 composite?

27 is odd, so 2 is not a factor. Try 3: 27 ÷ 3 = 9.
The factors of 27 are 1, 3, 9 and 27.
That is more than two factors.

Answer: Yes. 27 is composite: its factors are 1, 3, 9 and 27.

Example 2: A number that looks prime

Core

Is 91 prime or composite?

√91 ≈ 9.5, so test the primes 2, 3, 5 and 7.
91 is odd (not 2), its digit sum is 10 (not 3), and it does not end in 0 or 5 (not 5).
Try 7: 91 ÷ 7 = 13. So 91 = 7 × 13.

Answer: 91 is composite, because 91 = 7 × 13.

Example 3: Count composites in a range

Test-style

How many composite numbers are there from 20 to 30, including 20 and 30?

There are 11 whole numbers from 20 to 30.
Find the primes among them: 23 and 29. (21 = 3 × 7, 25 = 5 × 5, 27 = 3 × 9, and the even ones have factor 2.)
Every other number in the range is composite: 11 − 2 = 9.

Answer: There are 9 composite numbers from 20 to 30.

Common mistakes

✗ Mistake1 is composite, because it is not prime.

✓ Instead1 is neither prime nor composite. It has only one factor, itself.

The number 1 is neither prime nor composite. Composite numbers need more than two factors; 1 has just one.

✗ MistakeAll odd numbers are prime, so 21 is prime.

✓ Instead21 = 3 × 7, so 21 is composite.

Being odd only rules out the factor 2. Test 3, 5, 7 and the other primes too.

✗ Mistake2 is composite because it is even.

✓ Instead2 is prime: its only factors are 1 and 2.

Even numbers greater than 2 are composite because they have the extra factor 2. For 2 itself, that factor is the number.

Not to be confused with

Composite Numbervs.Prime number

A prime has exactly two factors, 1 and itself, like 13. A composite number has more, like 14 (1, 2, 7, 14).

Composite Numbervs.Even number

Even numbers are divisible by 2. Every even number above 2 is composite, but composite numbers can also be odd, like 9 or 35.

Quick check: 3 questions

Question 1 of 3

Which number is composite?

Show answer and explanation

Answer: C. 21 = 3 × 7, so it has the factors 1, 3, 7 and 21. 2 and 13 are prime, and 1 is neither prime nor composite.

Question 2 of 3

Which statement is true?

Show answer and explanation

Answer: D. 1 has only one factor, so it is neither. The smallest composite number is 4, odd numbers such as 9 are composite, and 2 is prime.

Question 3 of 3

What is the smallest composite number?

Show answer and explanation

Answer: A. 4 = 2 × 2 has the factors 1, 2 and 4. 1 is neither, 2 is prime, and 9 is composite but larger than 4.

Composite Number: frequently asked questions

Is 1 a composite number?

No. A composite number must be greater than 1 and have more than two factors. The number 1 has only one factor, itself, so it is neither prime nor composite. Leaving 1 out also keeps prime factorizations unique: 12 is 2 × 2 × 3, with no extra 1s to add.

How do you know if a number is composite?

Look for any factor other than 1 and the number itself. Use divisibility rules first: even numbers are divisible by 2, digit sums that are multiples of 3 mean divisible by 3, and endings of 0 or 5 mean divisible by 5. Then try 7, 11, 13 and so on up to the square root. One factor found proves the number is composite.

Can a composite number be odd?

Yes. Many composite numbers are odd: 9 = 3 × 3, 15 = 3 × 5, 35 = 5 × 7 and 91 = 7 × 13. An odd number just has no factor of 2; it can still have other factors. Only even numbers are automatically composite, and that is true only above 2.

Practice and tools

Effortless Math practicePractice on Effortless Math Prime Factorization CalculatorBreak any composite number into primes GCF and LCM CalculatorUse factors of composite numbers to find GCF and LCM

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 4.OA.B.4

Cite this entry

Effortless Math Team. “Composite Number.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/composite-number/

Flashcard

TermComposite Numbermore than two factors

DefinitionA whole number greater than 1 with more than two factors. 12 is composite: 1, 2, 3, 4, 6, 12. 1 is neither.

Study the full deck

Browse all terms in the Math Dictionary · More number system terms · Random term

Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5FactorA factor is a number or expression that divides another number or expression evenly, with no remainder. Factors multiply together to make a product: 4 × 6 = 24, so 4 and 6 are factors of 24. Every whole number greater than 1 has at least two factors, 1 and itself.Number System · Grade 4, Grade 5, Grade 6Prime NumberA prime number is a whole number greater than 1 with exactly two factors: 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13. The number 1 is not prime, and 2 is the only even prime number. Whole numbers greater than 1 that are not prime are composite.Number System · Grade 4, Grade 5, Grade 6Factor PairA factor pair is two whole numbers that multiply to give a certain number. The factor pairs of 12 are 1 × 12, 2 × 6 and 3 × 4. Listing factor pairs is a sure way to find every factor of a number: start at 1 and stop once the pairs begin to repeat.Number System · Grade 4, Grade 5, Grade 6Prime FactorizationPrime factorization is writing a whole number as a product of prime numbers only, such as 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3². Find it with a factor tree or repeated division. Every whole number greater than 1 has exactly one prime factorization, apart from the order of the factors.Number System · Grade 4, Grade 5, Grade 6Even NumberAn even number is an integer that can be divided by 2 with no remainder, so it can be split into two equal groups or into pairs. Even numbers end in 0, 2, 4, 6 or 8, such as 14, 236 and −10. Zero is even. Every even number can be written as 2n for some integer n.Number System · Grade 2, Grade 3, Grade 4NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Odd NumberAn odd number is a whole number that cannot be split into two equal groups: dividing it by 2 always leaves a remainder of 1. Odd numbers end in 1, 3, 5, 7 or 9, such as 7, 23 and 409. Every odd number can be written as 2k + 1, one more than a multiple of 2.Number System · Grade 2, Grade 3, Grade 4Divisibility RulesDivisibility rules are shortcuts that tell whether one whole number divides another with no remainder, without doing the division. A number is divisible by 2 if its last digit is even, by 3 if its digit sum is divisible by 3, by 5 if it ends in 0 or 5, and by 10 if it ends in 0.Number System · Grade 4, Grade 5, Grade 6Square RootA square root of a number is a value that, multiplied by itself, gives that number. The square root of 36 is 6 because 6 × 6 = 36. Every positive number has two square roots, such as 6 and −6, but the radical sign √ means the principal square root, which is the non-negative one.Number System · Grade 8, Algebra 1MultipleA multiple of a number is the result of multiplying that number by any whole number. The multiples of 4 are 4, 8, 12, 16, and so on, continuing without end. Every number is a multiple of itself and of 1. To test a number, divide: if the remainder is 0, it is a multiple.Number System · Grade 4, Grade 5, Grade 6Greatest Common FactorThe greatest common factor (GCF) is the largest factor shared by two or more numbers: the largest number that divides into both without a remainder. The GCF of 18 and 24 is 6. Find it by listing factors or by multiplying the prime factors the numbers share. The GCF is how you simplify fractions in one step.Number System · Grade 5, Grade 6, Grade 7Least Common MultipleThe least common multiple (LCM) is the smallest positive multiple shared by two or more numbers. The LCM of 6 and 9 is 18: it is the first number on both lists of multiples, 6, 12, 18, … and 9, 18, …. The LCM of the denominators is the least common denominator for adding fractions.Number System · Grade 5, Grade 6, Grade 7

Composite Number

What is a composite number?

Composite Number in a picture

Formal definition and notation

Key facts

Composite test: find one factor pair

Try it: test a number

Composite Number examples, step by step

Example 1: List the factors

Example 2: A number that looks prime

Example 3: Count composites in a range

Common mistakes

Not to be confused with

Quick check: 3 questions

Composite Number: frequently asked questions

Is 1 a composite number?

How do you know if a number is composite?

Can a composite number be odd?

Related terms

Practice and tools

Sources

Flashcard

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