# Prime Numbers and Composite Numbers

Prime Composite Numbers

In Mathematics, two types of numbers exist that rely on the factors they have. These two types of numbers are prime numbers and composite numbers. A prime number is a number which has only two factors i.e. one and itself whereas the composite number is a number which has more than two factors. In this article, we will study about what are prime numbers and composite numbers, prime composite numbers properties and the difference between both prime numbers and composite numbers

What are Prime Numbers and Composite Numbers?

Prime numbers are considered as the numbers which retain only two factors i.e. one and itself. It implies that the number can be divided only by 1 and itself. All prime numbers are an odd number apart from 2. Composite numbers are those numbers that retain more than two factors. It implies that the number except one and itself can be divided by other numbers also. Every non- prime number is a composite number.

List of Prime Numbers from 1 to 100

 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

Composite Numbers

The integer which can be obtained by multiplying the two smallest positive numbers and includes at least one divisor other than 1 is known as composite numbers. Composite numbers are neither a prime number nor a unit.

For example- 4, 6, 8, 9, 10…… are composite numbers because they have more than two factors.

Types of Composite Numbers

1. Odd Composite Numbers

2. Even Composite Numbers

Odd Composite Numbers

Every odd integer which is not a prime number is known as odd composite numbers. For example – 9, 15,21,25,27 and 31 are odd composite numbers.

Even Composite Number

Every even integer which is not a prime number is known as even composite numbers. For example, -4, 6,8,10, and 12 are even composite numbers.

List of Composite Numbers from 1 to 100

 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 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 85 86 87 88 90 91 92 93 94 95 96 98 99 100

Prime Numbers

A prime number is a positive integer which has only two factors i.e. one and itself. It implies that the number can be divided only by one and itself.

For example – 2, 3, 5, 7, 11….etc are some of the prime numbers

Prime Numbers Facts

•  The number 2 is only an even prime number. Other even numbers can be divided by 2. So the even numbers which can be divided by 2 are not a prime number.
• Zero and 1 are not a prime number
• The numbers o and 1 are neither considered as a prime number nor a composite number
• Not a single prime number greater than 5 ends with a 5. Since, any number greater than 5 that ends with 5 can be easily divided by 5. So, it cannot be considered as a prime number.

Solved Examples

1. Find if Number 53 is Considered as a Prime Number or Not.

Solution: Factors of 53 are 1 and 53.

The number 53 is divided by only two numbers that are 1 and itself.

Hence, 53 is a prime number

2. Is 6 a Prime Number or Composite Number?

Solution: Factors of 6 are 1,2,3,6

6 can be easily divided by 1, 2, 3, and 6 itself

6 is a composite number as it can be divided by more than 2 numbers except 1 and itself.

Fun Facts

• Number 1 is neither considered as a prime nor a composite number
• All even numbers apart from 2 are composite numbers
• The only even prime number is 2. All other prime numbers can be divided by 2
• Prime numbers are sometimes used in cryptography and security for technology and the internet.
• The largest prime number known till now has around 13 million digits.
• The Greek Mathematician Euclid examined prime numbers in 300 BC.
• Any whole number greater than 1 is either considered as a prime or composite number.
• The most interesting sequence of prime in which each digit have circle in them are: 6089, 60899, 608999, 6089999, 60899999, 608999999

Quiz Time

1. How Many Composite Numbers are There Between 1 to 100?

a.  72

b. 74

c.  75

d. 70

2. A Number that is Neither a Prime nor Composite

a.  6

b.  9

c.  1

d.  3

3.Which all Numbers are Considered as Prime Numbers Between 50 and 59 are:

a. 53 and 59

b. 51 and 59

c.  53 and 57

d. None of these

1. What are the Properties of Prime Numbers and Composite Numbers?

Properties of Prime Numbers

1. Prime numbers have only two factors i.e. one and itself

2. The method of finding the prime numbers is called integer factorization or prime factorization.

3. Prime numbers are those numbers that cannot be divided by other numbers except one and itself.

4. For a number to be considered as a prime number, it should be a non-zero whole number.

5. Every number greater than 1 can be divided easily by at least one prime number.

Properties of Composite Numbers

1. Composite numbers are the set of natural numbers which have 3 or more than 3 factors

2. A number 4 is the smallest composite number

3. A composite number with three different factors is known as sphenic number

4. Every composite number can be written as the product of two or more prime numbers.

5. Number “1” is not considered as a composite number

6. All even numbers except 2 are composite numbers

2. What is the Difference Between Prime Number and Composite Numbers?

The Differences Between Prime Composite Numbers are Given Below:

 Prime Numbers Composite Numbers Prime numbers are the numbers which have only 2 factors i.e. 1 and itself Composite numbers are the numbers which have at least 3 or more than 3 factors Prime numbers can only be divided by 1 and itself Composite numbers can be divided by any other number including 1 and itself. 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.