Prime and composite numbers: Class 6 practice
A prime number has exactly two factors, 1 and itself. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Multiplication tables
- Divisibility rules
The idea behind prime and composite numbers
A prime number has exactly two factors, 1 and itself. A composite number has more than two factors. 1 is neither. To test a number, try dividing by primes up to its square root.
Step-by-step method
- List primes up to √n.
- Try dividing n by each.
- If none divide exactly, n is prime; otherwise write one factor pair.
Worked example 1 (Basic)
Is 51 prime or composite? Justify.
- Check primes up to √51 ≈ 7.1
- 51 = 3 × 17
- Answer: Composite (3 × 17)
Worked example 2 (Standard)
Is 149 prime or composite? Justify.
- Check primes up to √149 ≈ 12.2
- None divides exactly
- Answer: Prime
Worked example 3 (Challenge)
Is 393 prime or composite? Justify.
- Check primes up to √393 ≈ 19.8
- 393 = 3 × 131
- Answer: Composite (3 × 131)
Common mistakes and misconceptions
- Calling 1 prime
- Calling every odd number prime (e.g. 91 = 7 × 13)
Practice questions
- (Basic) Is 39 prime or composite? Justify.
- (Basic) Is 41 prime or composite? Justify.
- (Standard) Is 133 prime or composite? Justify.
- (Standard) Is 65 prime or composite? Justify.
- (Challenge) Is 323 prime or composite? Justify.
- (Challenge) Is 347 prime or composite? Justify.
Answer key with full working
- Q1: Check primes up to √39 ≈ 6.2 → 39 = 3 × 13 → Answer: Composite (3 × 13)
- Q2: Check primes up to √41 ≈ 6.4 → None divides exactly → Answer: Prime
- Q3: Check primes up to √133 ≈ 11.5 → 133 = 7 × 19 → Answer: Composite (7 × 19)
- Q4: Check primes up to √65 ≈ 8.1 → 65 = 5 × 13 → Answer: Composite (5 × 13)
- Q5: Check primes up to √323 ≈ 18.0 → 323 = 17 × 19 → Answer: Composite (17 × 19)
- Q6: Check primes up to √347 ≈ 18.6 → None divides exactly → Answer: Prime
Syllabus note
This skill is listed under "Playing with Numbers" for Class 6 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is prime and composite numbers in?
"Playing with Numbers", Class 6 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.