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. For example, 7 is prime (only 1 × 7), while 12 is composite (1, 2, 3, 4, 6, 12 are all factors). Knowing whether a number is prime or composite is fundamental to factoring, finding GCF and LCM, and simplifying fractions. This concept is covered in Saxon Math, Course 2, as part of 7th grade math and is a building block for all number theory work in middle school.
Key Concepts
Property A counting number greater than $1$ is either prime or composite. A prime number has exactly two different factors: $1$ and itself. A composite number has three or more factors. The number $1$ is neither prime nor composite.
Examples The number $13$ is prime because its only factors are $1$ and $13$. The number $18$ is composite because its factors are $1, 2, 3, 6, 9,$ and $18$. The number $1$ is neither prime nor composite, as it has only one factor.
Explanation Think of prime numbers as exclusive clubs with only two members allowed: the number itself and $1$. Composite numbers are like giant parties where anyone who is a factor can join in the fun. And poor number $1$? It’s a club of one, so it doesn't fit in either group, making it truly unique in the number world!
Common Questions
What is a prime number?
A prime number is a counting number greater than 1 that has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23.
What is a composite number?
A composite number is a counting number greater than 1 that has more than two factors. Examples: 4 (factors: 1, 2, 4), 12 (factors: 1, 2, 3, 4, 6, 12), 15 (factors: 1, 3, 5, 15).
Is 1 a prime number?
No. The number 1 is neither prime nor composite. By definition, prime numbers must have exactly two factors, but 1 only has one factor (itself).
Is 2 a prime number?
Yes. 2 is the only even prime number. It has exactly two factors: 1 and 2. All other even numbers are composite because they are divisible by 2.
How do you determine if a number is prime?
Test whether any number from 2 up to the square root of the number divides it evenly. If none do, it’s prime. For 29: check 2, 3, 4, 5 (since √29 ≈ 5.4) — none divide evenly, so 29 is prime.
When do students learn about prime and composite numbers?
Prime and composite numbers are introduced in 4th–5th grade and extended in 7th grade, where students use prime factorization to find GCF and LCM.
Which textbook covers prime and composite numbers?
Saxon Math, Course 2 covers prime and composite numbers.