Composite Numbers

Composite numbers are numbers with more than two factors. Numbers can be classified on the basis of the number of factors that they have. If a number has just two factors - 1 and the number itself, then it is a prime number. However, most numbers have more than two factors, and they are called composite numbers. On this page, we will learn the difference between prime and composite numbers, the smallest composite number, and odd composite numbers. The last one is interesting because there are several odd composite numbers, unlike 2, which is the only even prime number.

A number that is divisible by a number apart from 1 and the number itself, is called a composite number. For example, 4 is a number that is divisible by 1, 2, and 4, therefore, it is a composite number.

Composite Number Definition

Composite numbers can be defined as natural numbers that have more than two factors.

Meaning of Composite Number

Composite number means a number that is divisible by smaller positive numbers apart from 1 and itself. For example, 6 is a composite number because it is divisible by 1, 2, 3, and 6. However, 19 is not a composite number because it is divisible by only two numbers 1 and 19 itself. There is no other number that divides 19, so, 19 is a prime number. Let us learn more about composite numbers with examples.

Examples of Composite Numbers

4, 6, 8, 9, and 10 are the first few composite numbers. Let us take 6 and 8. In the above example, 6 and 8 are called composite numbers because they have more than 2 factors. Let us proceed to understand the important properties of composite numbers.

In order to find a composite number, we find the factors of the given number. If the number has more than two factors, then it is composite. The best way to figure out a composite number is to perform the divisibility test. The divisibility test helps us to determine whether a number is a prime or a composite number. Divisibility means that a number is divided completely (with no remainder) by another number, other than 1 and itself.

To do this, we need to check to see if the number can be divided by these common factors: 2, 3, 5, 7, 11, and 13. If the given number is even, then start checking with the number 2. If the number ends with a 0 or 5, then check it by 5. If the number cannot be divided by any of these given numbers, then the number is a prime number. For example, 68 is divisible by 2, which means it has factors other than 1 and 68, so, we can say 68 is a composite number.

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Note the properties of a composite number listed below:

• All composite numbers are completely divisible by smaller numbers that can be prime or composite.
• Every composite number is made up of two or more prime numbers.

Let us have a look at the properties of the composite number 72 in order to understand the concept in a better way.

This figure shows that by multiplying these positive integers we get a composite number.

First 10 Composite Numbers

The first 10 composite numbers can be listed as 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18. All these numbers have factors other than 1 and the number itself. If we start counting from 1, we know that 1 is neither a prime number nor a composite number. Then 2 and 3 are prime numbers, so we start with 4 as the first composite number. In the same way, if we asked to list the first five composite numbers, we can list them as follows:

First Five Composite Numbers

The first five composite numbers are 4, 6, 8, 9, and 10.

The two main types of composite numbers in math are odd composite numbers and even composite numbers. Let us have a look at the two of them individually:

Odd Composite Numbers

All the odd numbers which are not prime are odd composite numbers. For example, 9, 15, 21, 25, 27 are odd composite numbers. Consider the numbers 1, 2, 3, 4, 9, 10, 11, 12 and 15. Here 9 and 15 are the odd composite numbers because these two odd numbers have more than 2 factors and they fulfill the condition of composite numbers.

Even Composite Numbers

All the even numbers which are not prime are even composite numbers. For example, 4, 6, 8, 10, 12, 14, and 16, are even composite numbers. Consider the numbers 1, 2, 3, 4, 9, 10, 11, 12, and 15 again. Here 4, 10, and 12 are the even composite numbers because these even numbers have more than 2 factors and they fulfill the condition of composite numbers.

The smallest composite number is 4. A composite number is defined as a number that has divisors other than 1 and the number itself. Now, as we start counting: 1, 2, 3, 4, 5, 6, .... so on, we see that 1 is not a composite number because its only divisor is 1. And 2 is not a composite number because it has only two divisors, i.e., 1 and the number 2 itself. 3 is not a composite number because it has only two divisors, i.e., 1 and the number 3 itself. However, when we come at number 4, we know that its divisors are 1, 2, and 4. So, the number 4 satisfies the criteria of a composite number. Therefore, 4 is the smallest composite number.

Difference Between Prime and Composite Numbers

A number that is divisible by a number other than 1 and the number itself, is called a composite number. This means that composite numbers have more than 2 factors. For example, 4 and 6 are composite numbers. Whereas, a number that is divisible only by 1 and itself is called a prime number, like, 2, 3, and 5. This means that a prime number has only 2 factors, 1 and the number itself.

☛ Related Articles

• Real Numbers
• Whole Numbers
• Rational Numbers
• Irrational Numbers
• Prime and Composite Numbers Worksheets

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What are Composite Numbers in Math?

Composite numbers are those numbers that have more than two factors. In other words, composite numbers have factors other than 1 and itself. For example, the number 6 is a composite number because it has 1, 2, 3, and 6 as its factors.

How to Find Composite Numbers?

To find whether a given number is composite, we just find the number of factors it has. If it has more than 2 factors, then the number is composite. For example, 4 has three factors, 1, 2, and 4. So, it is a composite number.

Is 2 a Composite Number?

No, 2 is not a composite number, it is the only even prime number. A composite number has more than two factors, other than 1 and the number itself. Here, 2 has only two factors, 1 and 2 itself. Therefore, 2 is a prime number.

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.

What are Prime and Composite Numbers?

A number that is divisible by a number other than 1 and the number itself, is called a composite number. For example, 4 and 6 are composite numbers. Whereas, a number that is divisible only by 1 and itself is called a prime number, like, 2, 3, and 5.

What is an Odd Composite Number?

All the odd numbers (excluding 1) which are not prime are odd composite numbers. For example, 9 and 15 are the odd composite numbers.

What is the Smallest Composite Number?

A composite number has more than two factors, other than 1 and the number itself. Here, 4 satisfies this condition, and there is no other number smaller than 4 which is composite. Therefore, 4 is the smallest composite number.

What is the Difference Between a Prime and a Composite Number?

A prime number has only two factors, 1 and the number itself, whereas, a composite number has more than two factors. For example, 5 has only two factors, 1 and 5, so it is a prime number. Whereas 6 has four factors, 1, 2, 3, and 6, so it is a composite number.

What are Consecutive Composite Numbers?

Consecutive composite numbers are those composite numbers that continuously follow each other without any prime number in between. For example, the first few consecutive composite numbers can be listed as 4, 6, 8, 9 10, and so on.

How many Composite Numbers are there from 1 to 100?

There are 74 composite numbers from 1 to 100. They can be listed as follows, 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.

What Composite Numbers are Between 6 and 11?

The composite numbers between 6 and 11 are 8, 9 and 10 because these numbers have more than 2 factors. The rest of the numbers between 6 and 11 are prime numbers, i.e., 7 is a prime number.

Which of the Factors of 120 are Composite Numbers?

The factors of 120 can be listed as, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120. Among these, the composite numbers are 4, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

What are the First Four Composite Numbers?

The first four composite numbers can be listed as 4, 6, 8, and 9. These numbers are called composite numbers because they have more than two factors.

Which is the Smallest Odd Composite Number?

The smallest odd composite number is 9 because if we start checking the composite numbers from 4, 6 and 8, we see that these are even numbers. Hence the smallest odd composite number is 9.

Which is the First Composite Number?

The first composite number is 4 because if we start checking the natural numbers we get 1 which is neither prime nor composite, then 2 and 3 are prime numbers. Therefore, the first composite number is 4.

What are the First Five Composite Numbers?

The first five composite numbers can be listed as 4, 6, 8, 9, and 10. These numbers have more than 2 factors, therefore they are called composite numbers. The natural numbers before 4 are 1, 2 and 3 in which we know that 1 is neither prime nor composite, then 2 and 3 are prime numbers. Therefore, the first five composite numbers are 4, 6, 8, 9, and 10.