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Skill: Classify numbers as prime, composite, or neither

Explanation and Free Practice Resources

Prime and composite classification distinguishes positive whole numbers by their factors: a prime has exactly two distinct positive factors, 1 and itself; a composite has more than two; and 1 is neither because it has only one positive factor. For numbers from 1 through 100, factor pairs, arrays, and divisibility relationships represent this structure; larger-number primality methods and extensions to negative, fractional, or other numbers are outside this scope, which supports later work with factorization, multiples, and fractions.

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Detailed Explanation: Classify numbers as prime, composite, or neither

A prime number has exactly two positive factors: 11 and the number itself.

A composite number has more than two positive factors.

The number 11 is neither prime nor composite because it has only one positive factor: 11.

Example: Classify 1818

List the factor pairs of 1818:

1×181 \times 18 2×92 \times 9 3×63 \times 6

So the positive factors of 1818 are:

1, 2, 3, 6, 9, 181,\ 2,\ 3,\ 6,\ 9,\ 18

There are more than two factors, so 1818 is composite.

Remember:

  • Exactly two factors →\rightarrow prime
  • More than two factors →\rightarrow composite
  • Only one factor, as with 11 →\rightarrow neither

Learn by doing: Classify numbers as prime, composite, or neither

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