Grade 6 Math: Prime and Composite Numbers

Grade 6 focus: A prime number is a whole number greater than \(1\) whose only positive factors are \(1\) and itself. A composite number is a whole number greater than \(1\) that has more than two positive factors. The number \(1\) is neither prime nor composite.

Video lesson: Watch this Math with Mr. J introduction to prime and composite numbers.

Quick examples

• Prime: \(2, 3, 5, 7, 11, 13, \ldots\)
• Composite: \(4, 6, 8, 9, 10, 12, \ldots\)

How to test “prime or composite?”

1. Check divisibility by small primes (\(2, 3, 5, 7, \ldots\)) up to \(\sqrt{n}\).
2. If you find a factor other than \(1\) and \(n\), then \(n\) is composite.
3. If no such factor exists, \(n\) is prime.

Connection to factor trees

Prime factorization breaks a composite number into a product of primes. That skill supports GCF, LCM, and simplifying fractions.

Common mistakes

• Treating \(1\) as prime.
• Assuming all odd numbers are prime (\(9\) and \(15\) are not).
• Stopping after one failed divisibility test—always be systematic.

Fluency check

Classify \(29\) and \(39\). (\(29\) is prime; \(39 = 3 \times 13\) is composite.)