Composite Numbers – Numbers with More Than Two Factors

A composite number is any whole number greater than 1 that is not prime — meaning it has at least one factor other than 1 and itself. In other words, it can be divided by some number in between.

The word “composite” comes from the Latin componere, “to put together” — fitting, since a composite number is literally built by multiplying smaller factors together. Some composite numbers are especially rich in factors: the Indian mathematician Srinivasa Ramanujan studied what he called “highly composite numbers” in a 1915 paper — numbers with more factors than any smaller number. 12, 24, 36, 60, and 120 are all highly composite; 60, for instance, has 12 factors, more than any number smaller than it, which is exactly why ancient Babylonian and modern timekeeping alike settled on base-60 for dividing hours into minutes.

Definition

Examples

Composite Numbers from 1 to 30

Primes vs Composites vs 1

The Fundamental Theorem of Arithmetic

Every composite number can be expressed as a unique product of prime numbers. This is called the Fundamental Theorem of Arithmetic. For example, 60 = 2² × 3 × 5 — and no other prime factorization exists for 60.

Why Composites Matter

• They are the numbers we break apart in prime factorization.
• Identifying composites helps us find GCF and LCM.
• Many encryption schemes rely on the difficulty of factoring large composites.

Key Takeaways

Practice: Composite Numbers