Composite number
A composite number is a counting number greater than 1 that has more than two factors—meaning it can be divided evenly by numbers other than just 1 and itself. For example, 9 is composite because its factors are 1, 3, and 9. Covered in Chapter 6 of Saxon Math Intermediate 4, identifying composite numbers is the essential counterpart to understanding prime numbers, and this skill underpins factoring, fraction simplification, and number theory in middle school.
Key Concepts
Property A counting number with more than two factors is a composite number. The number 4 is a classic example of a composite number because it has three factors: 1, 2, and 4. If a counting number greater than 1 is not prime, then it must be composite.
Example The number 9 is composite because it has three factors (1, 3, and 9) since $1 \times 9 = 9$ and $3 \times 3 = 9$. The number 10 is composite because it can be divided by 2 and 5, giving it the factors 1, 2, 5, and 10. We can show 8 is composite by making a $2 \times 4$ rectangle, proving it has factors other than 1 and 8.
Explanation Composite numbers are the social butterflies! Unlike primes, they have more than two factors and can be formed by multiplying different pairs of numbers. For instance, the number 12 is very composite because you can make it with $2 \times 6$ or $3 \times 4$. They are 'composed' of smaller factors, which is an easy way to remember the name.
Common Questions
What is a composite number?
A composite number is a whole number greater than 1 that has more than two factors. For example, 12 is composite because it can be divided by 1, 2, 3, 4, 6, and 12.
How do you tell if a number is composite?
Try dividing it by small numbers (2, 3, 5, 7). If any divide evenly other than 1 and the number itself, it is composite. For example, 15 ÷ 3 = 5, so 15 is composite.
What is the difference between prime and composite numbers?
A prime number has exactly two factors: 1 and itself. A composite number has three or more factors. The number 1 is neither prime nor composite.
When do students learn about composite numbers?
Composite numbers are introduced in Grade 4, Chapter 6 of Saxon Math Intermediate 4, alongside prime numbers as part of factor and divisibility work.
Is every even number greater than 2 composite?
Yes. Every even number greater than 2 is divisible by 2 (in addition to 1 and itself), giving it at least three factors, which makes it composite.
How do composite numbers connect to fractions?
Composite numbers can be factored into prime factors, which is essential for simplifying fractions. Knowing the factors of numerator and denominator lets you cancel common factors.