A composite number can be broken into smaller factors. Take 12: it divides evenly by 1, 2, 3, 4, 6, and 12. Because it has more than two factors, it is composite. A prime number, by contrast, has exactly two factors: 1 and itself.

The number 1 is neither prime nor composite. Every composite number can be written as a product of primes in exactly one way, apart from order. This is the fundamental theorem of arithmetic, and it makes primes the building blocks of the integers.

Composite numbers appear throughout number theory. Tests for primality and factorization are central to cryptography. RSA encryption, for example, relies on the difficulty of factoring large composite numbers. Sieve methods, from Eratosthenes onward, identify composites by eliminating multiples of primes. The concept is simple, but its consequences run deep.

• Positive integer with more than two factors
• Can be factored into primes
• 1 is neither prime nor composite
• Central to cryptography and number theory