Prime and Composite Numbers
Prime and composite numbers are fundamental number theory concepts in Grade 8 math (Yoshiwara Core Math). A prime number greater than 1 is divisible only by 1 and itself — examples: 2, 3, 5, 7, 11, 13. A composite number greater than 1 has additional factors; 12 = 2 × 2 × 3 is composite. The number 1 is neither prime nor composite. Prime numbers are the building blocks of all counting numbers through prime factorization. Identifying primes and composites is essential for fraction simplification, LCM/GCF computations, and algebraic factoring.
Key Concepts
Property A counting number (larger than 1) that is evenly divisible only by 1 and itself is called a prime number. A counting number larger than 1 that is not prime is called composite.
Examples The number 17 is prime because its only factors are 1 and 17. The number 25 is composite because it is divisible by 5, in addition to 1 and 25. Its factors are 1, 5, and 25. The number 2 is the smallest prime number and the only even prime. All other even numbers are composite because they are divisible by 2.
Explanation Think of prime numbers as basic building blocks; they only have two factors, 1 and themselves. Composite numbers are built from primes and can be divided by more than just 1 and themselves. The number 1 is neither prime nor composite.
Common Questions
What is a prime number?
A counting number > 1 divisible only by 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
What is a composite number?
A counting number > 1 with factors besides 1 and itself. Examples: 4, 6, 9, 12.
Is 1 prime or composite?
Neither. Prime and composite apply to counting numbers greater than 1.
How do you determine if a number is prime?
Try dividing by all primes up to its square root. If none divide evenly, it is prime.
Why is 2 the only even prime?
All other even numbers are divisible by 2, giving an extra factor. Only 2 has exactly two factors: 1 and 2.
What is prime factorization?
Expressing a composite number as a product of primes. For example, 12 = 2² × 3.