Determine whether a number is composite

A composite whole number greater than 1 has more than two positive factors and can be represented as a product of two smaller whole numbers, or as a rectangular array with more than one possible factor pair. Determining compositeness involves finding a nontrivial factor pair and distinguishing composite numbers from prime numbers; 1 is neither prime nor composite. This understanding is limited to classifying whole numbers within the elementary range, not advanced factorization or tests for very large numbers.

Detailed Explanation: Determine whether a number is composite

A whole number greater than $1$ is composite if it has more than two positive factors. A quick way to check is to find a factor pair: two whole numbers greater than $1$ that multiply to make the number.

Example: Is $18$ composite?

Look for two whole numbers that multiply to $18$ .

2 \times 9 = 18

The factors $2$ and $9$ are both smaller than $18$ , so this is a nontrivial factor pair.
Therefore, $18$ can be arranged into a rectangle with $2$ rows and $9$ columns. It has more than one factor pair:

1 \times 18 \quad \text{and} \quad 2 \times 9

Since $18$ has more than two positive factors, it is composite.

Remember: A number with exactly two positive factors is prime, and $1$ is neither prime nor composite.

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Is the Number Prime or Composite

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