Prime and Composite Numbers
Numbers can be grouped into two types based on how many factors they have: prime numbers and composite numbers. Understanding this classification is a key step in learning about factors, multiples, and number theory.
A prime number has exactly two factors, while a composite number has more than two factors. The number 1 is neither prime nor composite.
What is Prime and Composite Numbers - Class 4 Maths (Factors and Multiples)?
A prime number is a whole number greater than 1 that has exactly two factors: 1 and the number itself. Examples: 2, 3, 5, 7, 11, 13.
A composite number is a whole number greater than 1 that has more than two factors. Examples: 4, 6, 8, 9, 10, 12.
The number 1 is special — it has only one factor (itself), so it is neither prime nor composite.
Types and Properties
Prime Numbers up to 30:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Composite Numbers up to 30:
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30
Special Facts:
- 2 is the smallest prime number.
- 2 is the only even prime number. All other even numbers are composite.
- 4 is the smallest composite number.
- Every composite number can be written as a product of prime factors (prime factorisation).
Solved Examples
Example 1: Example 1: Identify Prime or Composite
Problem: Is 7 a prime number or a composite number?
Solution:
Step 1: Find all factors of 7.
Step 2: 7 = 1 × 7. No other pair of numbers multiplies to give 7.
Step 3: Factors of 7 = 1, 7 (exactly 2 factors).
Answer: 7 is a prime number.
Example 2: Example 2: Identify Prime or Composite
Problem: Is 12 a prime number or a composite number?
Solution:
Step 1: Find all factors of 12.
Step 2: 12 = 1 × 12, 2 × 6, 3 × 4
Step 3: Factors of 12 = 1, 2, 3, 4, 6, 12 (6 factors, more than 2).
Answer: 12 is a composite number.
Example 3: Example 3: Is 1 Prime or Composite?
Problem: Is 1 a prime number or a composite number?
Solution:
Step 1: Factors of 1 = 1 (only one factor).
Step 2: A prime number needs exactly 2 factors. A composite number needs more than 2.
Step 3: 1 has only 1 factor.
Answer: 1 is neither prime nor composite.
Example 4: Example 4: Is 2 Prime or Composite?
Problem: Is 2 a prime number or a composite number?
Solution:
Step 1: Factors of 2 = 1, 2 (exactly 2 factors).
Step 2: Since 2 has exactly two factors, it is prime.
Answer: 2 is a prime number. It is the smallest and only even prime number.
Example 5: Example 5: List All Prime Numbers Between 10 and 25
Problem: List all prime numbers between 10 and 25.
Solution:
Step 1: Check each number from 11 to 24:
- 11: factors = 1, 11 → Prime
- 12: factors = 1, 2, 3, 4, 6, 12 → Composite
- 13: factors = 1, 13 → Prime
- 14: factors = 1, 2, 7, 14 → Composite
- 15: factors = 1, 3, 5, 15 → Composite
- 16: factors = 1, 2, 4, 8, 16 → Composite
- 17: factors = 1, 17 → Prime
- 18: factors = 1, 2, 3, 6, 9, 18 → Composite
- 19: factors = 1, 19 → Prime
- 20: factors = 1, 2, 4, 5, 10, 20 → Composite
- 21: factors = 1, 3, 7, 21 → Composite
- 22: factors = 1, 2, 11, 22 → Composite
- 23: factors = 1, 23 → Prime
- 24: factors = 1, 2, 3, 4, 6, 8, 12, 24 → Composite
Answer: The prime numbers between 10 and 25 are 11, 13, 17, 19, 23.
Example 6: Example 6: Prime Factorisation of a Composite Number
Problem: Write 18 as a product of prime factors.
Solution:
Step 1: 18 ÷ 2 = 9
Step 2: 9 ÷ 3 = 3
Step 3: 3 ÷ 3 = 1
Answer: 18 = 2 × 3 × 3
Example 7: Example 7: Word Problem
Problem: Arjun has 13 chocolates. Can he share them equally among his friends (more than 1 friend) with none left over?
Solution:
Step 1: Factors of 13 = 1, 13
Step 2: 13 is a prime number. The only way to divide 13 equally is into 1 group of 13 or 13 groups of 1.
Answer: No, Arjun cannot share 13 chocolates equally among more than 1 friend (unless each friend gets exactly 1).
Example 8: Example 8: Checking a Larger Number
Problem: Is 29 prime or composite?
Solution:
Step 1: Check if any number from 2 to 5 divides 29 (we check up to roughly the square root of 29).
Step 2: 29 ÷ 2 = 14.5 (not exact), 29 ÷ 3 = 9.67 (not exact), 29 ÷ 5 = 5.8 (not exact).
Step 3: No number divides 29 exactly.
Answer: 29 is a prime number.
Example 9: Example 9: Twin Primes
Problem: Find all pairs of twin primes between 1 and 20. (Twin primes are two prime numbers that differ by 2.)
Solution:
Step 1: Prime numbers between 1 and 20: 2, 3, 5, 7, 11, 13, 17, 19
Step 2: Check pairs that differ by 2:
- 3 and 5: 5 − 3 = 2 → Twin primes
- 5 and 7: 7 − 5 = 2 → Twin primes
- 11 and 13: 13 − 11 = 2 → Twin primes
- 17 and 19: 19 − 17 = 2 → Twin primes
Answer: The twin prime pairs between 1 and 20 are (3, 5), (5, 7), (11, 13), (17, 19).
Key Points to Remember
- A prime number has exactly 2 factors: 1 and itself.
- A composite number has more than 2 factors.
- 1 is neither prime nor composite.
- 2 is the smallest prime and the only even prime number.
- 4 is the smallest composite number.
- Every composite number can be expressed as a product of prime factors.
- To check if a number is prime, test divisibility by primes up to its approximate square root.
Practice Problems
- Classify each number as prime or composite: 11, 15, 21, 23, 27.
- List all prime numbers between 30 and 50.
- Write the prime factorisation of 24.
- Is 49 prime or composite? Explain.
- Meera says that all odd numbers are prime. Is she correct? Give an example to support your answer.
- Find the smallest composite number that is odd.
- How many prime numbers are there between 1 and 20?
Frequently Asked Questions
Q1. What is a prime number?
A prime number is a whole number greater than 1 that has exactly two factors: 1 and the number itself. Examples include 2, 3, 5, 7, and 11.
Q2. What is a composite number?
A composite number is a whole number greater than 1 that has more than two factors. Examples include 4, 6, 8, 9, and 12.
Q3. Why is 1 not a prime number?
A prime number must have exactly two different factors. The number 1 has only one factor (itself), so it does not meet the definition of a prime number. It is neither prime nor composite.
Q4. Is 2 a prime number?
Yes. 2 is the smallest prime number and the only even prime number. Its only factors are 1 and 2.
Q5. Are all odd numbers prime?
No. While many prime numbers are odd, not all odd numbers are prime. For example, 9 (= 3 x 3), 15 (= 3 x 5), and 21 (= 3 x 7) are all odd but composite.
Q6. How do you check if a number is prime?
Try dividing the number by all prime numbers up to its approximate square root. If none of them divide it exactly, the number is prime. For example, to check 29, test divisibility by 2, 3, and 5. None divide 29 exactly, so 29 is prime.
Q7. What is prime factorisation?
Prime factorisation means writing a composite number as a product of prime numbers. For example, 12 = 2 x 2 x 3. Every composite number has a unique prime factorisation.
Q8. What are twin primes?
Twin primes are pairs of prime numbers that differ by exactly 2. Examples include (3, 5), (5, 7), (11, 13), and (17, 19).
Q9. Is this topic covered in the NCERT Class 4 syllabus?
Yes. Prime and composite numbers are introduced in Class 4 under the chapter Factors and Multiples. Students learn to identify prime numbers, composite numbers, and perform basic prime factorisation.
