**Prime and composite numbers** are the two types of numbers, that differ based on the number of factors they have. A prime number is the one that has only two factors and a composite number has more than two factors. A factor is a value, that can divide a number or an expression evenly. In this lesson, the properties of prime numbers and composite numbers are given along with their difference, examples and tables. The chart of prime and composite numbers, given in this article, will help to identify them easily.

## What are Prime Numbers and Composite Numbers?

A prime number is a number which has exactly two factors i.e. ‘1’ and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer. 1 is not a prime or composite number. Apart from these two, there is also a similar category of numbers which are coprime numbers. A detailed explanation of these numbers is given below.

### Prime Numbers

A prime number is the one which has exactly two factors, which means, it can be divided by only “1” and itself. But “1” is not a prime number.

**Example of Prime Number**

3 is a prime number because 3 can be divided by only two number’s i.e. 1 and 3 itself.

- 3/1 = 3
- 3/3 = 1

In the same way, 2, 5, 7, 11, 13, 17 are prime numbers.

### Composite Numbers

A composite number has more than two factors, which means apart from getting divided by the number 1 and itself, it can also be divided by at least one integer or number. We don’t consider ‘1’ as a composite number.

**Example of Composite Number**

12 is a composite number because it can be divided by 1, 2, 3, 4, 6 and 12. So, the number ‘12’ has 6 factors.

- 12/1 = 12
- 12/2 =6
- 12/3 =4
- 12/4 =3
- 12/6 =2
- 12/12 = 1

### Types of Composite Numbers

There are two types of composite numbers:

- Even composite numbers
- Odd composite numbers

### Odd Composite numbers

The odd positive integers or the odd numbers that are not prime numbers are called odd composite numbers. For example, 9, 21, 33, 45, etc., are odd composite numbers.

### Even Composite numbers

The even numbers that are not prime numbers are called even composite numbers. For example, 4, 10, 16, 28, 56, etc., are even composite numbers.

### What are Coprime Numbers?

Thecoprime-numbersor mutually primes or relatively primes are the two numbers which have only one common factor, which is 1. Let us understand the concept with an example.

Suppose there are two numbers, 14 and 15. Find whether both are coprime or not.

- The factors of 14 are 1, 2 and 7
- The factors of 15 are 1, 3 and 5.

For both the numbers, we can see, the common factor is 1. Therefore, 14 and 15 are coprime numbers. But if we consider another number say, 21, whose factors are 1, 3 and 7. Then, 21 is neither a coprime for 14 nor for 15.

### Smallest Composite Number

As you have understood already about the composite number, now let us know the smallest number which is composite in nature. If we see the list of composite numbers, it starts from 4, 6, 8, 9, 10, 12, 14, 15, and so on. So you can see here 4 is the smallest number, which has factors apart from 1 and itself, such as;

Factors of 4 are 1, 2, and 4.

## Prime and Composite Numbers List

The list of prime numbers from 1 to 100 are:

2 | 3 | 5 | 7 | 11 |

13 | 17 | 19 | 23 | 29 |

31 | 37 | 41 | 43 | 47 |

53 | 59 | 61 | 67 | 71 |

73 | 79 | 83 | 89 | 97 |

The list of composite numbers from 1 to 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

## Prime and Composite Numbers Chart

Identify the number of prime numbers given in the chart below and also with the help of this table, students can identify the list of composite numbers from 1 to 100.

**Note:**Numbers highlighted in yellow colour, are prime numbers while others are composite numbers.

From the given chart you can see the smallest prime number is 2 and the smallest composite number is 4.

## How to find if a number is prime or composite?

There are a few tricks and methods to remember if a given number is a prime or a composite number. We can use division method and Divisibility Rulesto find if a number is divisible by one or more number. Also we have prime factorisation method to find the prime factors of composite numbers. Let us find out:

- If a number is divisible by another number (other than 1), then it is a composite number
- Any even number greater than 2 is a composite number
- A number greater than 2 and multiple of 2 is not a prime number but a composite number
- In the same way, multiples of any number other than 1, are not a prime number
- If the prime factorisation results in the product of two or more prime numbers, then it is a composite number
- We can use divisibility rules to check if a number is divisible by any other number or not

## Related Articles

- Composite Numbers
- Prime Numbers
- Prime Numbers from 1 to 1000
- Prime Factorization
- Prime Factors
- Difference between Prime, Composite And Even, Odd Numbers
- Co-Prime Numbers
- How to Find Prime Numbers?

## Video Lesson on Prime Numbers

## Solved Examples on Prime and Composite Numbers

**Q.1: Find if 81 is a prime number or composite number.**

Solution: Given, the number is 81

Since, it is an odd number, thus we can check dividing 81 by the smallest odd prime number, i.e., 3

81/3 = 27

Again 27 is an odd number, dividing it by 3, we get;

27/3 = 9

9 is an odd number and divisible by 3

9/3 = 3

And 3 is the factor of itself.

3/3/ = 1

Hence, 81 is divisible by 3, 9, 27, and 81. Thus, it is a composite number.

**Q.2: Is 127 a prime or composite number?**

Solution: Since 127 is an odd number, it is not divisible by 2

By the divisibility rule of 3, if the sum of digits of a number is divisible by 3, then the number is also divisible by 3.

127: 1 + 2 + 7 = 10

10 is not divisible by 3

127 is not divisible by 5 (since the unit place digit is not 0 or 5)

127 is not divisible by 7 (127/7 = 18.1425…)

127 is not divisible by 11 (127/11 = 11.5454…)

In the same way, we can check to divide 127 by other prime numbers such as 13, 17, 19,…

At the end, we will find that 127 is not divisible by any other number apart from 1 and 127 itself.

Hence, 127 is a prime number.

Students can also practise by creating charts for prime and composite numbers from 1 to 1000.

## Practise Question

- Find if 89 is a prime number or composite number.
- What are the factors of 9?
- What is the prime factorisation of 36?
- Which of the following is a prime number?
- 6
- 19
- 27
- 63

## Frequently Asked Questions – FAQs

### What are the prime numbers from 1 to 10?

The prime numbers from 1 to 10 are 2, 3, 5, and 7

### What are the composite numbers from 1 to 10?

The composite numbers from 1 to 10 are 4, 6, 8 and 10.

### Is 6 a composite number?

Yes, 6 is a composite number, because it has more than two factors. They are 1, 2, 3, and 6.

### Is 17 composite or prime?

17 is a prime number, since it has two factors,i.e.,1 and 17.

### Is 0 a composite or prime?

0 is neither prime nor composite. Since, any number multiplied by 0 will be equal to 0. Thus, 0 will have infinite number of factors here. But a composite number will have finite number of factors

## FAQs

### What is prime and composite numbers with examples? ›

**Prime numbers can be written as the product of two numbers.** **Composite numbers can be written as the product of two or more than two numbers**. For example, 2,3,5,71,11… are prime numbers as they have only two factors i.e. one and itself. For example, 4,6,8,10,12… are composite numbers as they have more than two factors.

**What are composite numbers definition and examples? ›**

**All the natural numbers which are not prime numbers are composite numbers as they can be divided by more than two numbers**. For example, 6 is a composite number because it is divisible by 1, 2, 3 and even by 6.

**What are 5 composite numbers examples? ›**

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 number and composite numbers 1 to 100? ›**

So all the prime numbers that come within the range of 1 to 100 can be listed as, **2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97**. The remaining numbers in the range of 1 to 100 are composite numbers between 1 and 100.

**What are the prime numbers list? ›**

So, from the table, it is clear that **2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97** are the prime numbers.

**Is 47 a composite number? ›**

Is 47 a prime number? Yes, because its only factors are 1 and itself. Is 47 a composite number? **No, because it doesn't have proper factors**.

**What is a composite number simple definition? ›**

In math, composite numbers can be defined as numbers that have more than two factors. Numbers that are not prime are composite numbers because they are divisible by more than two numbers. Examples: Factors of 4 = 1, 2, 4 i.e.

**What is the definition of composite in math? ›**

A composite number is a positive integer. which is not prime (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16, ...

**What is an example of a composite? ›**

Composite – Composite building material examples include **concrete, reinforced plastics, cement, steel–reinforced concrete, and composite wooden beams**. These materials are generally durable and strong.

**What are the first 20 prime numbers? ›**

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Prime Numbers Facts: The only even prime number is 2 and the remaining even numbers can be divided by 2. So, it can't be a prime number.

### What are composite numbers give 3 examples? ›

The odd positive integers or the odd numbers that are not prime numbers are called odd composite numbers. For example, 9, 21, 33, 45, etc., are odd composite numbers.

**What are the prime and composite numbers from 1 to 50? ›**

We know a prime number has only two factors i.e. it is divisible by either 1 or by the number itself. 1 is neither prime nor composite. Prime numbers between 1 and 50 are **2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47**.

**How many composite numbers from 71 to 76? ›**

Answer sent to the myPAT Community Moderator. 75 & 76 have the same no of factors i.e. 6. Also, 71 & 73 are prime nos so they also have same no of factors, i.e. **2**.

**Is 52 prime or composite? ›**

The number 52 is a **composite number** and it has many factors other than one and the number itself. Factors of 52: 1, 2, 4, 13, 26, and 52.

**How to find a prime number? ›**

How do you know a prime number? If a number has only two factors 1 and itself, then the number is prime. Hence, **by prime factorisation of the given number**, we can easily determine a prime number.

**Why is 21 a composite number? ›**

The number 21 is a composite number. This is because **21 has more than two factors**. Its factors are 1, 3, 7, and 21, so 21 has four factors. Because 21 has more than two factors, it's a composite number.

**What are 24 prime numbers? ›**

So, the prime factorisation of 24 is 2 × 2 × 2 × 3 or 2^{3} × 3, where **2 and 3** are the prime numbers.

**Is 73 a mirror prime number? ›**

"**73 is the 21st prime number**," Sheldon explains. "Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3 ... and in binary 73 is a palindrome, 1001001, which backwards is 1001001."

**Is 23 a prime number or not? ›**

Is 23 a prime or composite number? **23 is a prime number** since it has only two factors, i.e. 1 and 23.

**Is 31 is a prime number or not? ›**

The **prime numbers** from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

### What is 10 example of composite number? ›

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 is composite meaning for kids? ›**

Composite numbers are **whole numbers that can be divided by numbers other than itself and 1**. They have “factors”. Factors are the numbers that divide into it. For example, 2 and 5 are factors of 10. Every whole number higher than 1 is either a composite number or a prime number.

**What is your definition of a composite number? ›**

a number that is a multiple of at least two numbers other than itself and 1.

**What is a prime and composite in math? ›**

**A prime number has only two factors, itself and one.** **A composite number has at least three factors, and sometimes a lot more**. Prime & Composite Numbers.

**What is the full meaning of composite? ›**

/ˈkɑːm.pə.zɪt/ **something that is made of various different parts**: The main character in her latest novel is a composite of several public figures of that era. Scientists have put together a composite picture of what the earth's crust is like.

**What are the four types of composite? ›**

The four pri- mary categories of composites are **polymer matrix composites (PMCs), metal matrix compos- ites (MMCs), ceramic matrix composites (CMCs), and carbon matrix composites (CAMCs)**.

**What are composites and give any two examples? ›**

**Cement-bonded wood fibre**: Mineralised wood pieces cast in cement. This composite has insulating and acoustic properties. Fibreglass: Glass fibre combined with a plastic which is relatively inexpensive and flexible. Carbon Fibre reinforced polymer: Carbon fibre set in plastic which has a high strength-to-weight ratio.

**What are the two types of composite? ›**

There are several different types of composites used today. The most common are: **Fibre reinforced composites.** **Particulate reinforced composites**.

**How many types of composite are there? ›**

There are **three major types of composites** based on matrix constituents. In each of these systems, the matrix is typically a continuous phase throughout the component.

**What is a sentence for composite? ›**

Examples from Collins dictionaries

**Spain is a composite of diverse traditions and people**. The commonest composites in current use are plastics, reinforced by glass or carbon fibers. Fiber-reinforced plastic is a composite made of a polymer matrix reinforced with fibers.

### Is 47 a prime number or not? ›

The number 47 has only two factors, i.e. 1 and 47 so **it is a prime number**.

**Why is 69 not a prime number? ›**

The number 69 is a composite number. Its factors are 1, 3, 23, and 69. **Because 69 has more than two factors**, it is a composite number rather than a prime number.

**Are all prime numbers odd? ›**

First, **except for the number 2, all prime numbers are odd**, since an even number is divisible by 2, which makes it composite. So, the distance between any two prime numbers in a row (called successive prime numbers) is at least 2.

**Why is 21 a prime number? ›**

No, 21 is not a prime number. The number 21 is divisible by 1, 3, 7, 21. For a number to be classified as a prime number, it should have exactly two factors. **Since 21 has more than two factors, i.e. 1, 3, 7, 21, it is not a prime number**.

**How is 13 a prime number? ›**

A prime number is a whole number greater than 1 with only two factors – itself and 1. A prime number cannot be divided by any other positive integers without leaving a remainder, decimal, or fraction. An example of a prime number is 13. **Its only divisors are 1 and 13**.

**Is 12 a prime number or composite? ›**

Is 12 a Composite Number? Yes, since 12 has more than two factors i.e. 1, 2, 3, 4, 6, 12. In other words, 12 is a composite number because 12 has more than 2 factors.

**How many prime and composite numbers are there between 100 to 200? ›**

101, 103, 107, 109, 113, 127, 131, 137, 139,149,151,157, 163, 167, 173, 179, 181, 191, 193, 197, 199. These are the **21 prime numbers** included in the set of numbers 100 to 200.

**How many composite numbers are there in 1 to 100? ›**

There are **74** numbers between the 1 to 100 composite numbers.

**Is 49 a composite number? ›**

Is 49 a prime number? **No, 49 is a composite number** because it has more than 2 factors.

**What are the composite numbers 60 to 90? ›**

Hence, composite numbers between 60 and 90 are **29 - 7 = 22** . Q. How many composite numbers are there in the first 10 natural numbers?

### How is 57 a composite number? ›

Is 57 a Composite number? Yes, the number 57 is composite since **it has more than 2 factors and they are 1, 3, 19, and 57**. That means 57 is exactly divisible by other numbers apart from 1 and the number itself.

**What is the largest 2 composite number? ›**

Answer and Explanation: The largest 2-digit composite number is **99**. The number 99 is also the largest two-digit number. It is a composite number because its factors are: 1, 3, 9, 11, 33, and 99.

**How is 81 a composite number? ›**

The number 81 is a composite number. **It has the factors 1, 3, 9, 27, and 81**. A composite number is a number that has more than two factors. Since 81 has 5 factors, it is a composite number.

**What is the composite of 66? ›**

Is 66 a Composite Number? Yes, since 66 has more than two factors i.e. **1, 2, 3, 6, 11, 22, 33, 66**. In other words, 66 is a composite number because 66 has more than 2 factors.

**What is the composite number of 72? ›**

As the number 72 is a composite number, it has many factors other than one and the number itself. Thus the factors of 72 are **1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72**. Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

**How do I find out if a number is prime or composite? ›**

**A prime number is a number which has exactly two factors i.e. '1' and the number itself**. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer.

**Is 44 a prime number? ›**

**No, 44 is not a prime number**. The number 44 is an even composite number. Apart from one and the number itself, 44 has many factors.

**Why is 27 not a prime number? ›**

Is 27 a prime number? No. **27 is divisible by other numbers (3 and 9), so it is not prime**. The factors of 27 are 1, 3, 9, and 27, so it is not prime.

**Is 21 a composite or prime number? ›**

As we know, 21 is a **composite number**, and it has prime factors.

**What is the composite of 29? ›**

Is 29 a Composite Number? No, since 29 has only two factors, i.e. 1 and 29. In other words, **29 is not a composite number** because 29 doesn't have more than 2 factors.

### How to calculate a prime number? ›

To prove whether a number is a prime number, **first try dividing it by 2, and see if you get a whole number**. If you do, it can't be a prime number. If you don't get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number (see table below).

**Why is 9 a prime number? ›**

**9 is not a prime number**. It can be divided by 3 as well as 1 and 9. The prime numbers below 20 are: 2, 3, 5, 7, 11, 13, 17, 19.

**Why is 23 a prime number? ›**

23 is a prime number since **it has only two factors**, i.e. 1 and 23.

**Why is only 2 prime number? ›**

Why is 2 a prime number? 2 is a prime number **because its only factors are 1 and itself**.

**Is 69 a prime number or composite? ›**

The number 69 is a **composite number**. Its factors are 1, 3, 23, and 69. Because 69 has more than two factors, it is a composite number rather than a prime number.

**Why is 15 not a prime number? ›**

15 is not a prime number because the factors of 15 are 1, 3, 5 and 15 ( 1 × 15 = 15 , 3 × 5 = 15 ). 15 has more than 2 factors, so it is not a prime number. 1 is not a prime number as it only has one factor - itself.

**Why is 45 a prime number? ›**

No, 45 is not a prime number. The number 45 is divisible by 1, 3, 5, 9, 15, 45. For a number to be classified as a prime number, it should have exactly two factors. **Since 45 has more than two factors, i.e. 1, 3, 5, 9, 15, 45, it is not a prime number**.

**Is 37 a prime or composite number? ›**

As we know, 37 is a **prime number**, it has only two factors, i.e. 1 and 37.