Composite Numbers for Class 6: Definition and Solved Examples

Composite numbers are natural numbers greater than 1 that have more than two factors. In simple words, a composite number can be divided by numbers other than 1 and itself. In this topic, students will learn how to identify composite numbers using factors, understand the difference between prime and composite numbers, and solve easy examples for better clarity. This helps build a strong foundation for future maths concepts like factors, multiples, and number classification.

Table of Contents

• What are Composite Numbers?
• How to Find If a Number Is Composite
• Properties of Composite Numbers
• Types of Composite Numbers
• Composite Numbers vs Prime Numbers
• Solved Example on Composite Numbers for Class 6
• Practice Questions on Composite Numbers for Class 6

What are Composite Numbers?

A composite number is a natural number greater than 1 that has more than two factors. In other words, it can be divided evenly not just by 1 and itself, but by at least one other whole number.

Examples:

• 6 can be divided by 1, 2, 3, and 6, it has 4 factors  ⇒  it is a composite number

• 7 can only be divided by 1 and 7, it has exactly 2 factors, 1 and the number itself ⇒  it is a prime number

The word ‘composite’ comes from the Latin 'compositus', meaning ‘put together’ or ‘made up of parts’. A composite number is literally made up of smaller numbers multiplied together.

What Is NOT a Composite Number?

• 1 is neither prime nor composite. It has only one factor, itself. The definition of both prime and composite numbers requires the number to be greater than 1, so 1 sits in its own special category.

• Prime numbers are not composite. Numbers like 2, 3, 5, 7, 11, and 13 have exactly two factors each (1 and themselves), so they don't qualify as composite.

• 0 is not a composite number. Zero is not a natural number in the standard counting sense, and divisibility rules don't apply to it the same way.

How to Find If a Number Is Composite

Here are two reliable methods for identifying whether a number is a composite number or not:

Method 1: Find the Factors

List out all the factors of the number. If you find more than two, it is a composite number.

Example: Is 18 composite?

Factors of 18: 1, 2, 3, 6, 9, 18. 18 has 6 factors. Therefore, 18 is a composite number.

Method 2: Divisibility Test

Try dividing the number by small primes: 2, 3, 5, 7, 11, 13...

If it's divisible by any number other than 1 and itself, it is a composite number.

Example: Is 91 composite?

91 = 7 × 13, so 91 is composite.

Properties of Composite Numbers 

Here are a few important properties of composite numbers:

• Every composite number has at least three factors. These always include 1, the number itself, and at least one other factor.

• Composite numbers can be written as a product of prime numbers. This is known as the Fundamental Theorem of Arithmetic: every composite number has a unique prime factorisation. For example: 12 = 2 × 2 × 3 = 2² × 3

• All even numbers greater than 2 are composite. Since they're all divisible by 2, they can't be prime.

• Composite numbers are evenly distributed but become less frequent as numbers grow larger, as the gaps between primes tend to increase.

• The smallest composite number is 4.

• A composite number is divisible by at least one prime number.

Types of Composite Numbers

Composite numbers fall into two broad types:

1. Even Composite Numbers

These are composite numbers that are also even, i.e., divisible by 2.

Examples: 4, 6, 8, 10, 12, 14, 16, 18, 20...

All even numbers greater than 2 are composite (since they're all divisible by 2). So there are infinitely many even composite numbers.

2. Odd Composite Numbers

These are composite numbers that are odd and not divisible by 2. They're divisible by odd primes like 3, 5, 7, etc.

Examples: 9, 15, 21, 25, 27, 33, 35, 39, 45…

Composite Numbers vs Prime Numbers

Here's a side-by-side comparison of composite and prime numbers.

 

 

Solved Example on Composite Numbers for Class 6

Example 1: Is 45 a composite number?

Solution: Factors of 45 are 1, 3, 5, 9, 15 and 45. There are 6 factors for 45. Therefore, 45 is a composite number. 

Example 2: Is 51 a prime or composite number?

Solution: 51 = 3 × 17. So 51 is a composite number.

Example 3: Is 4 a prime or composite number?

Solution: Factors of 4 are 1, 2, and 4. Since it has three factors, it's not prime. Therefore, 4 is a composite number.

Example 4: Write all composite numbers between 20 and 30.

Solution: Numbers from 21 to 29:

21 = 3 × 7 ⇒ composite

22 = 2 × 11 ⇒ composite

23: only divisible by 1 and 23 ⇒ prime

24 = 2³ × 3 ⇒ composite

25 = 5 × 5 ⇒ composite

26 = 2 × 13 ⇒ composite

27 = 3³ ⇒ composite

28 = 2² × 7 ⇒ composite

29: only divisible by 1 and 29 ⇒ prime

Composite numbers between 20 and 30: 21, 22, 24, 25, 26, 27, 28

Example 5: Is 97 a composite number?

Solution: Test divisors up to √97 ≈ 9.8, so check 2, 3, 5, and 7.

97 is odd (not ÷ 2)

9+7=16, not divisible by 3

Doesn't end in 0 or 5 (not divisible by 5)

97 ÷ 7 = 13.8... (not ÷ 7)

Therefore, 97 is prime, not composite.

Practice Questions on Composite Numbers for Class 6

1. List all composite numbers between 30 and 40.

2. Is 126 a composite number?

3. Is 49 prime or composite? How do you know?

4. What is the smallest odd composite number?

5. How many composite numbers are there between 1 and 20?

6. Identify whether 12 is a composite number or not.

7. Is 21 a composite number? Give reasons.

8. Find whether 25 is composite or not.

9. Which of the following numbers are composite: 2, 4, 5, 6, 8?

10. Is 1 a composite number? Explain your answer.