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G.2 Prime and composite numbers

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What are prime and composite numbers?

Prime numbers are whole numbers greater than 1 that have exactly two factors: 1 and the number itself. Composite numbers are whole numbers greater than 1 that have more than two factors.

Examples:
  • 2 is prime because its only factors are 1 and 2.
  • 9 is composite because its factors are 1, 3, and 9.
Note

The number 1 is neither prime nor composite because it has only one factor: 1.

How to identify prime and composite numbers

To decide if a number is prime or composite, check how many factors it has. A factor is a number that divides evenly into another number without leaving a remainder.

Steps:
  • Start with the number 1 and the number itself.
  • Test other numbers between them to see if they divide evenly.
  • If only 1 and the number divide evenly, it is prime.
  • If more numbers divide evenly, it is composite.
Note

Even numbers greater than 2 are always composite because they are divisible by 2.

Prime numbers up to 50

Here is a list of prime numbers between 1 and 50. These are good to memorize because they appear often in math problems.

Prime Numbers:
  • 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Note

2 is the only even prime number. Every other even number is divisible by 2 and therefore composite.

Using factors to check your work

Finding all factors of a number helps confirm if it is prime or composite. If a number has only two factors, it is prime. If it has three or more, it is composite.

Examples:
  • Factors of 7: 1, 7 → Prime
  • Factors of 12: 1, 2, 3, 4, 6, 12 → Composite
Note

You can use multiplication facts to find factors quickly. For example, 3 × 4 = 12, so 3 and 4 are factors of 12.

Why prime and composite numbers matter

Prime and composite numbers are important for understanding multiplication, division, and fractions. Prime numbers are the “building blocks” of all other numbers because every composite number can be written as a product of primes.

Example:
  • 12 = 2 × 2 × 3 (prime factors)
Note

This process is called prime factorization. It shows how a composite number can be broken into a product of prime numbers.