Prime and Composite Numbers

What are the prime and composite numbers?

Prime Numbers:

Prime numbers are those numbers which have only two factors 1 and the number itself. 

In other words, a number which is divisible by only itself and 1 is a prime number. So, prime number has only two different factors 1 and the number itself.

For example, these numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, etc which have only two factors i.e. 1 and the number itself.



Twin Primes:

If the difference between the two prime numbers is 2 they are called twin primes. For example (3, 5), (5, 7) and (11, 13) are set of twin primes. So, two consecutive prime numbers having only one number between them are called twin primes.


Co-Prime Numbers:

If two numbers have only 1 as a common factor, they are called as co-primes. For example (2, 3), (4, 5), (3, 7) and (4, 9) are co-primes.


Composite Numbers:

Composite numbers are those numbers which have more than two factors.

In other words, a number that has more than two different factors is a composite number. So, a composite number is also exactly divisible by numbers other than 1 and itself.

For example, 4 is a composite number and it can be divided by 1, 2 and 4.

6 is a composite number and it can be divided by 1, 2, 3 and 6.

8 is a composite number and it can be divided by 1, 2, 4 and 8.  

9 is a composite number and it can be divided by 1, 3 and 9.

Therefore, 1 is a unique number that is neither prime nor composite as it has only one factor.


Solved Example on Prime and Composite Numbers:

Identify prime numbers and composite numbers in the given numbers 3, 8, 17, 23, 25, 32, 41, 44.

3 = 3 × 1, factor of 3 are 3 and 1.

8 = 1 × 8, 8 = 2 × 4, factor of 8 are 1, 2, 4 and 8.

17 = 1 × 17, factor of 17 are 1 and 17.

23 = 1 × 23, factor of 23 are 1 and 23.

25 = 1 × 25, 25 = 5 × 5, factor of 25 are 1, 5 and 25.

32 = 1 × 32, 32 = 2 × 16, 32 = 4 × 8, factor of 32 are 1, 2, 4, 8, 16 and 32.

41 = 1 × 41, factor of 41 are 1 and 41.

44 = 1 × 44, 44 = 2 × 22, 44 = 4 × 11, factor of 44 are 1, 2, 4, 11, 22 and 44.

The numbers having only two factors are 3, 17, 23 and 41. Therefore, 3, 17, 23 and 41 are prime numbers. Composite numbers are 8, 25, 32, 36 and 44.



Questions and Answers on Prime and Composite Numbers

I. Choose the right answer and fill in the blank:

(i) The only even prime number is ….…..

(a) 0

(b) 2

(c) 4

(d) 6


(ii) The number which is neither prime nor even ….…..

(a) 1

(b) 2

(c) 10

(d) 100


(iii) The number which has more than 2 factors is called a ….…..

(a) Even

(b) Odd

(c) Prime

(d) Composite


(iv) ….….. is the smallest composite number.

(a) 0

(b) 2

(c) 3

(d) 4


(v) A prime number has only ….….. factors.

(a) 0

(b) 1

(c) 2

(d) 3


(vi) A pair of numbers that do not have any common factor other than 1 are ….….. numbers.

(a) Even

(b) Co-prime

(c) Twin prime

(d) Prime


(vii) The smallest odd prime number is:

(a) 1

(b) 3

(c) 5

(d) 7


(viii) Which of the following is a prime number?

(a) 9

(b) 11

(c) 21

(d) 15


(ix) Which of the following even number is prime?

(a) 2

(b) 4

(c) 16

(d) 26


(x) Which of the following is a composite number?

(a) 19

(b) 21

(c) 23

(d) 29


(xi) Number formed by multiplying the first three prime numbers is:

(a) 50

(b) 40

(c) 30

(d) 20


Answers:

(i) (b) 2

(ii) (a) 1

(iii) (d) Composite

(iv) (b) 2

(v) (c) 2

(vi) (b) Co-prime

(vii) (b) 3

(viii) (b) 11

(ix) (a) 2

(x) (b) 21

(xi) (c) 30


II. Write true or false:

(i) 1 is a prime number.

(ii) There are 8 prime numbers between 1 – 20.

(iii) 12 is a prime number.

(iv) 21 has 4 factors – 1, 3, 7 and 21.

(v) 4, 6, 7, 8 and 9 are composite numbers.

(vi) Consecutive numbers are always co-prime.


Answers:

(i) false

(ii) true

(iii) false

(iv) true

(v) false

(vi) true


III. Choose all prime numbers:

12           19            7             8             9           11           15          

13           24           27           23           34           37           36


Answers:

19, 7, 11, 13, 23, 37


IV. Write all the composite numbers less than 30.

Answers:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21,22, 24, 25, 26, 27, 28


V. Write all the prime numbers less than 20.

Answer:

2, 3, 5, 7, 11, 13, 17, 19


VI. Check if the given pair of numbers are co-primes:

(i) 15 and 38

(ii) 25 and 26

(iii) 12 and 18


Answers:

(i) co-primes

(ii) co-primes

(iii) not co-primes


VII. Fill in the blanks:

(i) The numbers with just 2 factors are called ……………………… numbers.

(ii) Smallest even prime number is ……………………….

(iii) Numbers with more than 2 factors are called ……………………… numbers.

(iv) 1 is neither ……………………… nor ……………………….

(v) All composite numbers have more than ……………………… factors.


Answers:

(i) prime

(ii) 2

(iii) composite

(iv) prime, composite

(v) 2



VIII. Circle all the composite numbers in the given box:

Circle all the Composite Numbers

Answers:

15, 9, 21, 49, 35, 3393, 51

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