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Chapter 3: Playing With Numbers

Exercise 3.1

1.  Find the sum of any two numbers ?

(a)  odd numbers

(b)  even numbers

SOLUTION (a)                               SOLUTION (b)

e.g.  6 + 3 = 9                                e.g.  12 + 14 = 26

 

2. Write down the prime numbers less than 20.

SOLUTION:

The numbers which are divisible by itself is known as prime numbers . prime numbers which are  less than 20 are,

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

 

3. Write down the composite numbers less than 20.

SOLUTION:

The numbers which are not prime numbers is known as composite numbers. The composite numbers  which are less than 20 are,

4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 18 .

 

4. The numbers 31 and 13 are prime numbers. Both these numbers have same digits 1 and 7. Find such pairs of prime numbers up to 100.

SOLUTION:

(79 , 97)   (37 , 73) (17 , 71)

 

5. Express the following in the form of sum of two odd primes.

SOLUTION :

(a)  24 = 5 + 19

(b)  44 = 7 + 37

(c)   18 = 7 + 11

(d)  36 = 31 + 5

 

6. Find any three pair of prime numbers whose difference is two.

SOLUTION:

Two prime numbers whose difference is ‘2’ is also called as twin primes or twin prime number.

3 pairs :        (41 , 43)      ( 73 , 71)    (5 , 3)

 

7. Express the following numbers in the form of sum of three odd primes.

SOLUTION:

(a)  53 = 31 + 3 + 19

(b)  61 = 19 + 11 + 31

(c)   31 = 19 + 5 + 7

 

8. Write down the 3 pairs of prime numbers which is less than 20 and also whose sum is divisible by 5.

SOLUTION:

(*)  17 + 3 = 20          (5  x  4 = 20. It is divisible by 5)

(*)  13 + 2 = 15           (5  x  3 = 15. It is divisible by 5)

(*)   11 + 19 = 30        ( 5  x  6 = 30. It is divisible by 5)

 

9. FILL IN THE BLANKS.

(*) 1 is neither  _____   nor ________.         ans: (composite , prime)

(*)   The number which has only one factor is called _________.    ans: (prime number)

(*)  The  smallest composite number is ________.   ans: ( 4 )

 

10.  TRUE OR FALSE.

(*) The sum of two prime numbers is always even.                              Ans : false

e.g.     3 + 2 = 5   (i.e) odd

(*)  The product of three odd numbers is odd.                         Ans :  true

e.g.     5 x 7 x 3 = 105   (i.e) odd

(*)  The product of two even numbers is always even.   Ans : true

e.g     2 x 4  = 8  (i.e) even

6 x 2 = 12 (i.e) even

 

 

Exercise 3.2

1. Find out the common factors of the following.

(a)  28 & 20

(b)  25 & 15

(c)   56 & 120

SOLUTION:

(a)  Factors of (20)  = 1  , 10 , 20, 2 , 4 ,5

Factors of (28)  = 7 , 14 , 28 ,1 , 2 , 4 ,

The factors that are common  are :  4, 2, 1

(b)  Factors of (15) = 1 , 15,3 , 5

Factors of (25) =  1 ,25,5

The factors that are common  are : 1 , 5.

(c)   Factors of  (56) = 1 , 14 , 28 , 56 ,2 , 4 , 7 , 8.

Factors of (120) =  1 ,30 ,40 , 10 ,12 , 2 ,3 ,4 ,5 ,6 ,8 , 15 ,20 ,24 ,60 , 120.

The  factors that are common are : 1 , 2 , 4 , 8 .

 

2. Find the numbers (all) which are less than 100  and also  common multiples of 4 & 3.

SOLUTION:

(*) multiples of 3 = 3, 15, , 6, 9, 12

(*) multiples of 4 = 4 ,8, 12, 16, 20

The Common multiples are   =  12, 36, 48,24, 60, 72, 84, 96.

3. From the given numbers , find which numbers are co prime numbers ?

(a)  68 and 17

(b)  16 and 81

(c)   35 and 18

SOLUTION:

(*)  68 and 17

Factors of 68 = 1, 2, 4, 17, 34, 68

Factors of 17 =  1, 17

The factors that are common are :  1 , 17

Since it has common factors other than 1, the above given 2 number is not a co prime.

(*) 16 and 81

Factors of 16 = 1, 2, 4, 8, 16

Factors of 81 = 1, 3, 9, 27, 81

The common factor is 1. Therefore the given two number is co prime.

(*) 35 and 18

Factors of 35 = 1, 5, 7, 35

Factors of 18 = 1, 2, 3, 6, 9, 18

Common factor is 1. Therefore the given two number is co prime.

 

4. A particular number is divisible by both 14 and 5. Find the other number that is always divisible.

SOLUTION:

Factors of 5 = 1 , 5

Factors of 14 = 1, 2, 7

The common factors of these numbers is 1. Therefore, the given two number is co prime number and also the number will be divisible by their product.

 

5. A number is divisible by 12. Find the other numbers, which are divisible of 12.

SOLUTION:

The factors are : 1, 2, 3, 4, 6 , 12

Therefore, the numbers 1,2,3,4,6  other than 12 by which this number is also divisible.

 

6. Find the common factors of the following given below:

(*)  4 , 8 and 12

(*)  5 , 15 , 25

SOLUTION:

(*)  4 , 8 and 12

Factors of 4   =  1 , 2 , 4

Factors of 8   =  1 , 2 , 4 , 8

Factors of 12 =  1 , 2 , 3 , 4 , 6 , 12

The common factors are  :  1, 2, 4.

(*)  5 , 15 , 25

The factors of 5 =   1  , 5

The factors of 15 =  1 , 3 , 5 , 15

The factors of 25 = 1 , 5 , 25

The common factors are : 1 , 5



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3 Comments

  1. manvinder kaur manvinder kaur
    May 26, 2018    

    Need help in solving the salybus of class 6th

  2. Amir ali Amir ali
    May 26, 2018    

    I like it.

  3. Nitin Singh Nitin Singh
    May 26, 2018    

    very helpful to complete notebook

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