What is a composite number? Definition, examples.

Composite numbers definition

  • A composite number is a positive integer that has at least one positive divisor other than 1 and the number itself.
  • Positive integers that are only dividing by themselves and 1 are called prime numbers.
  • A composite number is also any positive integer larger than 1 that is not a prime number.

Examples of composite numbers. Examples of numbers that are not composite, but prime.

  • According to the definition above, 1 is not a composite number; 1 is also not considered a prime number either, so the first composite number is 4 (composite numbers list starts by 4);
  • 2 is divisible only by 2 and 1, so 2 is a prime number;
  • 3 is divisible only by 3 and 1, so 3 is a prime number;
  • 4 is divisible by 4, 2 and 1, so 4 is not a prime number, it's a composite number; its prime factorization is 4 = 22;
  • 6 is divisible by 6, 3, 2 and 1, so 6 is not a prime number, it's a composite number; its prime factorization is 6 = 2 × 3;
  • 8 is divisible by 8, 4, 2 and 1, so 8 is not a prime number, it's a composite number; its prime factorization is 8 = 23;
  • 9 is divisible by 9, 3, and 1, so 9 is not a prime number, it's a composite number; its prime factorization is 9 = 32;
  • 10 is divisible by 10, 5, 2 and 1, so 10 is NOT a prime number;
  • 12 is divisible by 12, 6, 4, 3, 2 and 1, so 12 is NOT a prime number;

All the composite numbers, up to 100: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

There is no known simple formula that sets all of the prime numbers apart from composites.