Composite Numbers

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What are Composite Numbers?

Composite numbers can be defined as natural numbers that have more than two factors. Composite numbers are those natural numbers that are not prime and have more than two positive factors.

Natural numbers that are not prime are composite numbers, because they are divisible by more than two numbers.

Let’s learn more about composite numbers with examples..

Examples of Composite Numbers

4, 6, 8, 9 and 10 are the first few composite numbers.

Let's take 4 and 6

examples of composite numbers

In the above example- 4 and 6 are called "Composite" numbers because they are  "made by combining other numbers."

This idea is so important and we used it in a theorem called The Fundamental Theorem of Arithmetic.


Characteristics of Composite Numbers

A composite number is a positive integer that can be formed by multiplying two smaller positive integers.

Every positive integer is composite, prime, or the unit 1, so the composite numbers are evenly divisible by smaller numbers that can be prime, composite, and 1.

For a composite number, there are a minimum of two primes that can be multiplied together to make the number.

Example:

multiplying positive integers will give a composite number

While multiplying these positive integers we get a composite number.


Composite Numbers List from 1 to 100

Here is the list of composite numbers from 1 to  100

composite numbers list

Prime and Composite Numbers

  • When a number can be divided up exactly it is a Composite Number.
  • When a number cannot be divided up exactly it is a Prime Number.
  • Therefore, 6 is Composite, but 7 is Prime.

Different types of Composite Numbers

The two main types of composite numbers in maths are:

  • Odd Composite Numbers
  • Even Composite Numbers

Odd Composite Numbers

All the odd integers which are not prime are odd composite numbers.

Examples of composite odd numbers are 9, 15, 21, 25, 27 etc.

Consider the numbers 1, 2, 3, 4, 9, 10, 11, 12 and 15.

Here 9 and 15 are the odd composites because those two numbers have the odd divisors and satisfy the composite condition.

Even Composite Numbers

All the even numbers which are not prime are even composite numbers.

Examples of composite even numbers are 4, 6, 8, 10, 12, 14, 16, etc.

Consider the numbers 1, 2, 3, 4, 9, 10, 11, 12 and 15 again.

Here 4, 10 and 12 are the even composites because those two numbers have the even divisors and satisfy the composite condition.

Do you know about the smallest composite number? Let's talk about the smallest composite number.

Smallest Composite Number

Composite number is defined as a number that has divisors other than1 and the number itself.

Start counting : 1, 2, 3, 4, 5, 6, .... so on.

1 is not a composite number because its sole divisor is 1.

2 is not a composite number because it has only two divisors; i.e 1 and the number itself.

3 is not a composite number because it has only two divisors; i.e 1 and the number 3 itself.

Let’s look at number 4...

Its divisors are 1, 2 and 4.

Number 4 satisfies the criteria of a composite number.

So, 4 is the smallest composite number.

 
Thinking out of the box
Think Tank
  1. Is 21 a composite number?
  2. Is 72 a composite number?
  3. How many factors does 42 have?
  4. How many composite numbers are there in between 40 to 50?Think about

What are Composite Numbers from 1 to 100?

There are 74 composite numbers between 1 and 100 (including 1 and 100)

Composite numbers between 1 to 10 4, 6, 8, 9, 10
Composite numbers between 11 to 20 12, 14, 15, 16, 18, 20
Composite numbers between 21 to 30 21, 22, 24, 25, 26, 27, 28, 30
Composite numbers between 31 to 40 32, 33, 34, 35, 36, 38, 39, 40
Composite numbers between 41 to 50 42, 44, 45, 46, 48, 49, 50
Composite numbers between 51 to 100 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100

How to determine the Composite Numbers?

  • Find all the factors of a given number.
  • If the number has more than two factors, then it is composite.
  • The best way to figure out if it is a composite number is to perform the divisibility test.
  • The rule states that a number is divisible by any composite number- if it is divisible by each of its factors.
  • Performing the divisibility test will help you determine whether or not a number is a prime or composite number.
  • If the larger number is divisible by all factors, it is divisible by the composite number.

Let us explore the same using the following simulation.

  • Click on the box and type the required number.
  • If it is a composite number, it will show a message that it is a composite number.
  • It will also show a message if it is not a composite number.


Solved Examples

Example 1



 

Is 21 a composite number?

Solution:

Given number is 21

Its factors or divisors are -

1, 3, 7, 21

It has more than two factors.

\(\textit { ∴  21 is a composite number} \)
Example 2



 

Determine whether 486 is a composite number or not?

Solution:

Given number is 486

Its factors or divisors are -

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486

It has more than two factors.

\(\textit { ∴ 486 is a composite number} \)
 
tips and tricks
Common Mistakes
  1. Mistake: 2 is a composite number.

    Fact: A common mistake is to imagine 2 as a composite number as it is even.

    2 is a prime number having 1 and 2 as factors.

  2. Mistake: Every even number is a composite number.

    Fact: No, all even numbers are not composite numbers.

    There is one such even number that is not composite, the number 2.

Practice Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 

Important Topics

Given below are the list of topics that are closely connected to composite numbers. These topics will also give you a glimpse of how such concepts are covered in Cuemath.


Frequently Asked Questions (FAQs)

1. How to find composite numbers?

To find whether a given number is a composite, we just find its number of factors.

If it has more than 2 factors then the number is composite. You can find the examples under "Solved Examples”.

2. Is 2 a composite number?

A composite number has more than two factors.

In this case, 2 has only two factors i.e. 1 and 2.

Therefore, two is a prime number, not a composite number.

3. What are the composite numbers between 1 and 100?

The composite numbers between 1 and 100 are-

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

4. What is a composite number and prime number?

When a number can be divided up exactly it is known as Composite Number.

When a number cannot be divided up exactly it is known as the Prime Number.