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.


In other words, 

If two prime numbers can be paired with a difference of 2, that is they have one composite number between them, then the pair is called a twin prime.

For example; (3, 5), (5, 7), (11, 13), (17, 19), (41, 43), (59, 61), (71, 73), etc.


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.



Observe the following table.

Number

1

2

3

4

5

6

7

Factors

1

1,2

1, 3

1, 2, 4

1, 5

1, 2, 3, 6

1, 7

The numbers 2, 3, 5, ....... have only 2 factors, 1 and itself.

       Such numbers are called Prime numbers.


The numbers 4, 6, ...... have more than 2 factors.

      Such numbers are called Composite numbers.


Note:

(i) 1 is neither a prime nor a composite number.

(ii) 2 is the smallest prime number.

(iii) 2 is the only even prime number.

(iv) No prime number ends with zero or 5.


A prime number is a natural number which has only two different factors, 1 and the number itself. A composite number is a natural number which has more than two different factors.

Prime Numbers Between 1 and 100

The Sieve of Eratosthenes: This is a simple method to find out the prime numbers. This method was invented by a Greek astronomer Eratosthenes about 230 B.C.

Let us find all the prime numbers between 1 and 100.

Prime Numbers Between 1 and 100

Steps:

(i) 1 is not a prime number. Cross it.

(ii) 2 is a prime number. Circle 2 and cross out all the multiples of 2.

(iii) The next prime number is 3. Circle 3 and cross out all the multiples of 3.

(iv) The next prime number is 5. Circle 5 and cross out all the multiples of 5.

(v) The next prime number is 7. Circle 7 and cross out all the multiples of 73.

(vi) The next prime number is 11. Circle 11 and cross out all the multiples of 11.

(vii) The next prime number is 13. Circle 13 and cross out all the multiples of 13.

(viii) The next prime number is 17. Circle 17 and cross out all the multiples of 17.

(ix) The next prime number is 19. Circle 19 and cross out all the multiples of 19.

(x) The next prime number is 23. Circle 23 and cross out all the multiples of 23.

(xi) Continue the process till all the numbers are either circled or cross out.


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


IX. Write all the prime numbers between:

(i) 1 and 20

(ii) 20 and 40

(iii) 40 and 60

(iv) 60 and 80

(v) 80 and 100


Answer:

IX. (i) 2, 3, 5, 7, 11, 13, 17 and 19.

(ii) 23, 29, 31, 37.

(iii) 41, 43, 47, 53, and 59.

(iv) 61, 67, 71, 73, and 79.

(v) 83, 89 and 97.


X. Write all the composite numbers between 1 and 40.


Answer:

X. 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.


XI. Fill in the blanks:

(i) The smallest prime number is ................

(ii) The largest two-digits prime is  ................

(iii) Every prime number except  ................ is odd

(iv) ................ is neither a prime nor a composite number.

(vi) Since 4 has 3 factors, 4 is a  ................ number.


Answer:

XI. (i) 2

(ii) 97

(iii) 2

(iv) 1

(vi) composite


XII. State whether the following statements are true or false.

(i) There is only one natural number that is neither a prime nor a composite.

(ii) The odd number are prime numbers.

(iii) All even numbers are composite numbers.

(iv) The sum of two prime numbers is always an even number.

(v) 33 is a prime number.


Answer:

XII. (i) True

(ii) False

(iii) False

(iv) False

(v) False


Numbers.

Various Types of Numbers




5th Grade Math Problems

From Prime and Composite Numbers to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

    Feb 28, 24 04:07 PM

    Fraction 8/16
    There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1…

    Read More

  2. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 28, 24 01:43 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More

  3. Fraction as a Part of Collection | Pictures of Fraction | Fractional

    Feb 27, 24 02:43 PM

    Pictures of Fraction
    How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

    Read More

  4. Fraction of a Whole Numbers | Fractional Number |Examples with Picture

    Feb 24, 24 04:11 PM

    A Collection of Apples
    Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

    Read More

  5. Identification of the Parts of a Fraction | Fractional Numbers | Parts

    Feb 24, 24 04:10 PM

    Fractional Parts
    We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

    Read More