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It is crucial to understand the difference between prime and composite numbers in Mathematics. While composite numbers are numbers with more than two factors. They are just the opposite of prime numbers. Prime numbers are those that have just two factors, i.e. 1 and the number itself. A prime number is always a natural number. All the natural numbers that are not prime numbers fall into the category of composite numbers. So, composite numbers are divisible by more than two numbers. In this article, we will learn the following:
- What are prime and composite numbers?
- Difference between prime and composite numbers
- Properties of prime and composite numbers
- How to identify prime and composite numbers
- Facts about prime and composite numbers
- Composite numbers list
- Prime and composite numbers chart
What are Prime Numbers?
A prime number is a positive integer. It has exactly two factors, 1 and the number itself. So, if n is a prime number, its factors will be 1 and n itself. We can also define a prime number as a number that is a positive integer and is not a product of any other two positive integers other than the number itself and 1.
Interesting Prime Numbers
There are some interesting facts about prime numbers. Some of them are listed here.
| Prime Numbers |
| Smallest prime number is 2 |
| Largest Prime Number 2^(82,589,933) – 1 is the recent largest prime number. Mathematicians are still finding more. |
| Twin Primes The prime numbers whose difference is two are twin prime numbers. For example, 3 and 5, 5 and 7, 11 and 13 are sets of twin prime numbers. In other words, they are two consecutive prime numbers that have only one number between them. |
| Co-Prime Numbers Co-prime numbers are the two numbers that have only 1 as a common factor. For example, 2 and 3, 4 and 5, 3 and 7, 4 and 9 are co-prime numbers. |
Properties of Prime Numbers
The following are some properties of prime numbers:
- Every prime number is greater than 1
- Each prime number is a factor of itself
- Every number that is greater than 1 can be divided by at least one prime number.
- Every positive integer that is even and greater than 2 can be written as the sum of two prime numbers.
- 2 is the only even prime number.
- All prime numbers are odd except 2.
- Two prime numbers are coprime to one another.
- Every composite number can be factorized into prime factors.
Prime Numbers List
Here is a list of prime numbers from 1 to 100. Students can understand the concept of prime numbers from this list and create a list beyond 100 for practice.
| Prime Numbers List |
| 2, 3, 5, 7, 1, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 |
What are Composite Numbers?
Unlike a prime number, a composite number is a number that has more than two factors.
We can define composite numbers as the numbers that can be generated on multiplication of the two smallest positive integers and contain at least one more divisor in addition to the number ‘1’ and itself. All even numbers that are greater than 2 are amongst the many examples of composite numbers.
So, are all even numbers composite?
No, 2 is an even prime number. In fact, it is the only even number that is prime. Therefore, we cannot say that all even numbers are composite numbers.
Types of Composite Numbers
Composite numbers are of two types:
- Odd Composite Numbers
- Even Composite Numbers
Odd Composite Numbers
All odd numbers greater than 1 that are not prime are odd composite numbers.
The examples of odd composite numbers are 9, 15, 21, and more.
Even Composite Numbers
Even composite numbers include all even integers that are not prime numbers.
The examples of even composite numbers are 4, 6, 8, 10, and more.
Properties of Composite Numbers
The properties of composite numbers are as follows:
- Every composite number has more than two factors
- The factors evenly divide composite numbers
- Composite numbers are their own factors too.
- 4 is the smallest composite number
- Each composite number has at least two prime numbers as its factors.
- A composite number is divisible by other composite numbers too.
Composite Numbers List
Here is a list of all composite numbers from 1 to 100. Students can understand the concept of composite numbers from this list and create a list beyond 100 for practice.
| Composite Numbers List |
| 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 |
How to Find Composite Numbers?
You must find the factors of a number to determine if it is a composite number. If there are more than two factors, then the number is a composite number. We can perform the divisibility test to find whether a number is prime or composite.
In the divisibility test, we divide the number by common factors such as 2, 3, 5, 7, 11, and 13. If these factors fail to divide the number completely, then the number is a prime number. For example, 22 is divisible by 2, which means it has a factor 2 other than 1 and 22. Therefore, 22 is a composite number.
How to Find Prime Numbers?
There are two methods that help determine if given numbers are prime or composite numbers.
Method 1:
Apart from 2 and 3, you can write every prime number in the form of 6n + 1 or 6n – 1, where n is a natural number.
For example:
6(1) – 1 = 5
6(1) + 1 = 7
Method 2:
For determining a number more than 40 as a prime number, we can use the following formula:
n2 + n + 41, where n= 0, 1, 2, ….and above.
For example:
(0)2 + 0 + 41 = 41
(1)2 + 1 + 41 = 43
(2)2 + 2 + 41 = 47
Difference between Prime and Composite Numbers
There are multiple differences between prime numbers and composite numbers. The following tables enumerate some key differences between the two.
| Prime Numbers | Composite Numbers |
| They have 2 factors. One and the number itself. | They have more than two factors. |
| It can be written in the form of the product of two numbers. | They can be written as the product of two or more numbers |
| Example: The factors of 7 are 1 and 7. | Example: The factors of 6 are 1, 2, 3, and 6. |
Prime and Composite Numbers Chart
Earlier mathematicians used numerical tables to record all of the primes or prime factorizations. The sieve of Eratosthenes presented a list of prime numbers. This method provides a chart- Eratosthenes chart. The following chart shows prime numbers up to 100 in colored boxes. All numbers other than the colored boxes are composite numbers.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |
| 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |
| 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |
| 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |
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FAQs
Prime Numbers and Composite Numbers Explained | Turito? ›
The number 11 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors.
Why is 11 not a prime number? ›The number 11 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors.
Why is 8 not a prime number? ›Let us begin by defining what a prime number is: a prime number is a number that is divisible by only itself and 1. Since we know that 8 has more than two factors, then we can come to the conclusion that 8 is not a prime number and thus we say that 8 is a composite number.
Why is 2 a prime number? ›Why is 2 a prime number? 2 is a prime number because its only factors are 1 and itself.
Why is 1 not a prime number but 2 is? ›For a number to be called as a prime number, it must have only two positive factors. Now, for 1, the number of positive divisors or factors is only one i.e. 1 itself. So, number one is not a prime number. Note: 2 is the smallest number that satisfies the definition of prime numbers.
Why is 3 a prime number but not 6? ›For example, 3 is a prime number, because 3 cannot be divided evenly by any number except for 1 and 3. However, 6 is not a prime number, because it can be divided evenly by 2 or 3.
Why is 69 not a prime number? ›The divisors of 69 are \[1,3,23,69\]. So, the number 69 has more than two divisors. So, 69 is NOT a prime number.
Why is 77 not a prime number? ›No, 77 is not a prime number. The number 77 is divisible by 1, 7, 11, 77. For a number to be classified as a prime number, it should have exactly two factors. Since 77 has more than two factors, i.e. 1, 7, 11, 77, it is not a prime number.
Why is 27 not a prime number? ›Since 27 has more than two factors, i.e. 1, 3, 9, 27, it is not a prime number.
Why is 87 a composite number? ›Is 87 a Composite Number? Yes, since 87 has more than two factors i.e. 1, 3, 29, 87. In other words, 87 is a composite number because 87 has more than 2 factors.
Are all odd numbers prime? ›
No, every odd number is not a prime number. Example: 9 is an odd number having factors 1, 3 and 9 and is not a prime number.
How do you explain prime numbers? ›A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.
What is the smallest prime number? ›(i) 1 is the smallest prime number.
Why is ten not a prime number? ›Let us begin by defining what a prime number is: a prime number is a number that is divisible by only itself and 1. Since we know that 10 has more than two factors, then we can come to the conclusion that 10 is not a prime number and thus we say that 10 is a composite number.
Why 33 is not a prime number? ›Yes, 33 is a composite number as it has factors other than 1 and itself. It has factors 3 and 11 other than 1 and 33.
Why is 32 not a prime number? ›No, 32 is not a prime number. The number 32 is divisible by 1, 2, 4, 8, 16, 32. For a number to be classified as a prime number, it should have exactly two factors. Since 32 has more than two factors, i.e. 1, 2, 4, 8, 16, 32, it is not a prime number.
Why is 30 not a prime number? ›No, 30 is not a prime number. The number 30 is divisible by 1, 2, 3, 5, 6, 10, 15, 30. For a number to be classified as a prime number, it should have exactly two factors. Since 30 has more than two factors, i.e. 1, 2, 3, 5, 6, 10, 15, 30, it is not a prime number.
Why isn't 4 a prime number? ›Definition: A prime number is a whole number with exactly two integral divisors, 1 and itself. The number 1 is not a prime, since it has only one divisor. The number 4 is not prime, since it has three divisors ( 1 , 2 , and 4 ), and 6 is not prime, since it has four divisors ( 1 , 2 , 3 , and 6 ).
Why is 49 a composite number? ›Is 49 a Composite Number? Yes, since 49 has more than two factors i.e. 1, 7, 49. In other words, 49 is a composite number because 49 has more than 2 factors.
What is the biggest prime number ever found? ›The largest known prime number (as of May 2023) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.
Can a negative number be prime? ›
Answer One: No.
By the usual definition of prime for integers, negative integers can not be prime. By this definition, primes are integers greater than one with no positive divisors besides one and itself. Negative numbers are excluded.
So what is it - odd, even or neither? For mathematicians the answer is easy: zero is an even number.
Why 9 is not 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. Don't forget: the number 1 is not a prime number as it only has one factor.
Why is 7 not a prime number? ›The number 7 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors.
Why 51 is not a prime number? ›51 is not a prime number because it has 3 and 17 as divisors, as well as itself and 1. In other words, 51 has four factors.
What is the rarest prime number? ›The new prime number, known as M77232917, is one million digits larger than the previous record. It is also a particularly rare type of prime called a Mersenne prime, meaning that it is one less than a power of two. Three is a Mersenne prime because it is a prime and is equal to 22 – 1.
What number can never be a prime number? ›Zero and 1 are not considered prime numbers. Except for 0 and 1, a number is either a prime number or a composite number. A composite number is defined as any number, greater than 1, that is not prime.
Why is 91 not a prime number? ›So, 91 is divisible by 7 other than 1 and itself. Hence, it is not a prime number.
Why 7 11 13 7 is a composite number? ›Answer: The given numbers have more than 2 factors. Therefore, they are composite numbers.
Why 3 5 7 7 is a composite number? ›Given number is 3 × 5 × 7 + 7. 112 is an even number. Also, 112 is divisible by other numbers such as 2, 4, 7, 8, 14, 16, 28 and 56 apart from itself (112) and 1. So, 3×5×7+7 is a composite number.
How come 9 is not a prime number? ›
Let us begin by defining what a prime number is: a prime number is a number that is divisible by only itself and 1. Since we know that 9 has more than two factors, then we can come to the conclusion that 9 is not a prime number and thus we say that 9 is a composite number.
Why is 42 a composite number? ›As the number 42 is a composite number, it has many factors other than one and the number itself. The factors of 42 can be positive or negative, but it cannot be in decimal or fraction form. Therefore, the factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
Why 7 6 5 4 3 2 1 5 is a composite number? ›We know that a number is called a composite number if it has at least one factor other than 1 and the number itself. Here, 5045 is the product of 2 prime factors 5 and 1009 . Hence,7X 6 X 5 X 4 X 3 X 2 X 1+ 5 is a composite number.
Why is 8 not a composite number? ›8 is a Composite number because it can be divided by 1 ,2,4 and 8 itself. So, the number has four factors.
Why is 8 a composite number? ›Is 8 a Composite Number? Yes, since 8 has more than two factors i.e. 1, 2, 4, 8. In other words, 8 is a composite number because 8 has more than 2 factors.