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Prime, Composite Numbers and Their Arrangements

What is Prime Number?

Any Natural number greater than 1, which is divisible by 1 and only by itself is called Prime Number.

Example

2, 3, 5, 7, 11 etc.

Note

2 is the smallest Prime Number.

Arrangement of prime numbers

Prime numbers can be arranged in a line form like shown as below in the diagram.

Arrangement of prime numbers
Arrangement of prime numbers

What is composite number?

Any Natural number, which is greater than 1 and is not a Prime Number is called a Composite Number.

Example

4, 6, 8, 9, 10 etc.

Note

1 is neither a Prime Number nor Composite Number.

Note

Every number in maths can either be a prime or a composite number except 0 and 1 because 0 and 1 are neither a prime number nor a composite number.

Arrangement of composite numbers

Composite numbers can be arranged in a rectangular or square form like shown as below in the diagram.

Arrangement of composite numbers
Arrangement of composite numbers

What are coprimes?

Two numbers are called to be coprime or co-prime if they have only 1 as a common factor.

In other way, we can say if greatest common divisor of two numbers is 1, then the two numbers are coprimes.

Example

(2,3), (14,15), (8,13) etc.

What is twin prime?

Two numbers are called Twin Prime if they differ by 2 only or we can say that there is only one composite number between them. One prime number can be 2 more or 2 less than another prime number.

Example

(3,5), (29,31), (71,73) etc.

What are prime triplets?

A set of three consecutive Prime Numbers if the smallest and the largest differ by 6 and must be in the form of (p, p + 2, p + 6) is called a Prime Triplet.

Example

(5,7,11)
Why?
Because, 5, 7 and 11 is in the form of p, p + 2, p + 6
where p = 5
p + 2 = 5 + 2 = 7
and p + 6 = 5 + 6 = 11

Multiple Choice Questions

1) The greatest two digit prime number is.

a) 91

b) 97

c) 99

d) 93

2) The only prime number between 90 and 100 is

a) 97

b) 99

c) 93

d) 98

3) 79 and 89 both are ___________ numbers.

a) prime

b) composite

c) twin

d) unique

4) 2 and 3 are only ___________ prime numbers.

a) consecutive

b) twin

c) unique

d) odd

5) The smallest odd prime number is

a) 2

b) 3

c) 1

d) 4

6) The greatest one digit prime number is

a) 1

b) 2

c) 5

d) 7

7) Which of the following pair of numbers are not twin prime?

a) 41 and 43

b) 71 and 73

c) 53 and 59

d) 11 and 13

8) Which of the following pair of numbers are coprime?

a) 3 and 17

b) 17 and 68

c) 14 and 16

d) 13 and 91

9) The number of prime numbers between 50 and 100 are

a) 8

b) 10

c) 12

d) 6

10) The prime numbers between 70 and 80 are

a) 72, 73, 74

a) 71, 72, 73

a) 71, 74, 79

a) 71, 73, 79

Worksheet on Prime and Composite Numbers

Fill in the blanks

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twin
coprime
3
1
2
odd
composite
25
1
prime

1) Total number of even prime numbers is ___________.

2) The smallest prime number is ___________.

3) The number of primes between 0 and 100 is ___________.

4) The least odd prime number is ___________.

5) The pair of (71, 73) is called ___________ primes.

6) 138 is a ___________ number.

7) Every prime number except 2 is an ___________ number.

8) The pair of (14, 15) is called ___________.

9) Any two ___________ numbers are always coprime.

10) ___________ is neither prime nor composite number.