Problem Set 34 – Prime, Composite and Co-prime NumbersClass 5 Maths · Chapter 8 Multiples and Factors · Problem Set 34 – Maharashtra Board

Summary: Problem Set 34 – Prime, Composite and Co-prime Numbers

A prime number has exactly two factors: 1 and itself. 2, 3, 5, 7, 11 and 13 are prime.

A composite number has more than two factors. 4, 6, 8, 9 and 10 are composite.

1 has only one factor (itself), so 1 is neither prime nor composite.

2 is the only even prime number; every other even number has 2 as an extra factor.

Factors shared by two numbers are common factors. If the only common factor is 1, the numbers are co-prime, like 9 and 10.

Key points to remember

• Prime: exactly 2 factors (1 and itself)
• Composite: more than 2 factors
• 1 is neither prime nor composite
• 2 is the only even prime
• Primes up to 20: 2, 3, 5, 7, 11, 13, 17, 19
• Common factors are in both factor lists
• Co-prime: only common factor is 1
• Co-prime numbers need not be prime themselves

Problem Set 34 – Prime, Composite and Co-prime Numbers – Notes

1. Count the factors

• Factors of 5: 1, 5 → two factors. Factors of 9: 1, 3, 9 → three factors.
• Factors of 17: 1, 17 → two factors. Factors of 15: 1, 3, 5, 15 → four factors.
• 1 is a factor of every number.

2. Prime and composite numbers

• A number with only two factors, 1 and itself, is a prime number: 5, 17, 23.
• A number with more than two factors is a composite number: 9, 15, 28.
• To test a number, try dividing it by 2, 3, 5, 7… If one of them divides exactly, the number is composite.

3. The special numbers 1 and 2

• 1 has only one factor, so it is neither prime nor composite.
• 2 has factors 1 and 2 only, so it is prime. It is the only even prime.
• Every even number bigger than 2 also has 2 as a factor, so it is composite.

4. Common factors

• Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
• Numbers in both lists are common factors: 1, 2, 4, 8.

5. Co-prime numbers

• Two numbers are co-prime if their only common factor is 1.
• Factors of 9: 1, 3, 9. Factors of 14: 1, 2, 7, 14. Only 1 is common → 9 and 14 are co-prime.
• 16 and 24 share 1, 2, 4, 8 → not co-prime. Note: 9 and 14 are both composite, yet they are co-prime.

Formulas at a glance

Key terms

Problem Set 34 – Prime, Composite and Co-prime Numbers – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 34 – Prime, Composite and Co-prime Numbers – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 34 – Prime, Composite and Co-prime Numbers

⏱ About 25 minutes

1. Learn (5 min)
   Learn the meanings of prime, composite and co-prime, and remember that 1 is neither.
2. Sort (15 min)
   List all numbers from 1 to 50 and mark each one prime, composite or neither.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.