Composite Numbers Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Composite Numbers.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Integers greater than 1 that can be expressed as a product of two smaller positive integers; they are the opposite of primes.

Numbers that can be built by multiplying smaller numbers together.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Composite = 'composed' of prime factors. Not prime \neq composite (1 is neither).

Common stuck point: 1 is neither prime nor composite—it is a special case with exactly one factor (itself), so it fits neither category.

Sense of Study hint: Try to find even one factor other than 1 and the number itself. If you can, the number is composite. Use a factor tree to break it down.

Worked Examples

Example 1

easy
Determine whether 91 is prime or composite. If composite, find a factor pair.

Solution

  1. 1
    Test divisibility by primes up to \sqrt{91} \approx 9.5: primes to test are 2, 3, 5, 7.
  2. 2
    91 is odd (not divisible by 2). Digit sum = 10 (not divisible by 3). Last digit \neq 0, 5 (not by 5).
  3. 3
    Test 7: 91 \div 7 = 13. Yes! 91 = 7 \times 13.
  4. 4
    91 is composite with factor pair (7, 13).

Answer

91 is composite: 91 = 7 \times 13.
To test primality, check all primes up to \sqrt{n}. If none divide n, it is prime; if any divide n, it is composite. 91 is a classic 'looks prime' trap — many students guess prime because neither 7 nor 13 are obvious factors.

Example 2

medium
List all composite numbers between 20 and 35, and for each, give one non-trivial factor pair.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Is 1 composite? Is 4 composite? Is 2 composite? Explain each briefly.

Example 2

medium
How many composite numbers are there from 1 to 20? List them and explain why each is composite.
← Back to Composite Numbers Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

prime numbersfactors