Class 6 - Maths - Playing With Numbers

Exercise 3.1

Question 1.

Write all the factors of the following numbers:

(a) 24     (b) 15     (c) 21     (d) 27     (e) 12     (f) 20      (g) 18      (h) 23     (i) 36

 

Answer:

(a) 24 = 1 * 24 

      24 = 2 * 12

      24 = 3 * 8

      24 = 4 * 6

      24 = 6 * 4

So, the factors of 24 = 1, 2, 3, 4, 6, 12, 24

(b) 15 = 1 * 15 

      15 = 3 * 5

      15 = 5 * 3

So, the factors of 15 = 1, 3, 5, 15

(c) 21 = 1 * 21 

      21 = 3 * 7

      21 = 7 * 3

So, the factors of 21 = 1, 3, 7, 21

(d) 27 = 1 * 27 

      27 = 3 * 9

      27 = 9 * 3 

So, the factors of 27 = 1, 3, 9, 27

(e) 12 = 1 * 12 

      12 = 2 * 6

      12 = 3 * 4

      12 = 4 * 3

      12 = 6 * 2

So, the factors of 12 = 1, 2, 3, 4, 6, 12

(f) 20 = 1 * 20 

      24 = 2 * 10

      24 = 4 * 5

      24 = 5 * 4

      24 = 10 * 2

So, the factors of 20 = 1, 2, 4, 5, 10, 20

(g) 18 = 1 * 18 

      18 = 2 * 9

      18 = 3 * 6

So, the factors of 18 = 1, 2, 3, 6, 18

(h) 23 = 1 * 23 

So, the factors of 23 = 1, 23

(i) 36 = 1 * 36 

      36 = 2 * 18

      36 = 3 * 12

      36 = 4 * 9

36 = 6 * 6

So, the factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

Question 2.

Write first five multiples of:

(a) 5     (b) 8      (c) 9

 

Answer:

(a) 5 * 1 = 5, 5 * 2 = 10, 5 * 3 = 15, 5 * 4 = 20, 5 * 5 = 25

So, the first five multiple of 5 are: 5, 10, 15, 20 and 25

(b) 8 * 1 = 8, 8 * 2 = 16, 8 * 3 = 24, 8 * 4 = 32, 8 * 5 = 40

So, the first five multiple of 8 are: 8, 16, 24, 32 and 40

(c) 9 * 1 = 9, 9 * 2 = 18, 9 * 3 = 27, 9 * 4 = 36, 9 * 5 = 45

So, the first five multiple of 9 are: 9, 18, 27, 36 and 45

Question 3.

Match the items in column 1 with the items in column 2:

                    Column 1                          Column 2

                      (i) 35                           (a) Multiple of 8

                      (ii) 15                          (b) Multiple of 7

                     (iii) 16                          (c) Multiple of 70

                     (iv) 20                          (d) Factor of 30

                     (v) 25                           (e) Factor of 50

                                                          (f) Factor of 20

 

Answer:

                      Column 1                        Column 2

                      (i) 35                           (b) Multiple of 7

                      (ii) 15                          (d) Factor of 30

                     (iii) 16                          (a) Multiple of 8

                     (iv) 20                          (f) Factor of 20

                     (v) 25                           (e) Factor of 50

Question 4.

Find all the multiples of 9 up to 100.

 

Answer:

We have to find all the multiples of 9 up to 100

Now,  9 * 1 = 9, 9 * 2 = 18, 9 * 3 = 27, 9 * 4 = 36, 9 * 5 = 45, 9 * 6 = 54, 9 * 7 = 63, 9 * 8 = 72,

9 * 9 = 81, 9 * 10 = 90, 9 * 11 = 99

So, the multiple of 9 up to 100 are:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

 

                                                                     Exercise 3.2

Question 1.

What is the sum of any two:

(a) Odd numbers

(b) Even numbers.

 

 Answer:

(a) The sum of any two odd numbers is an even number.

Example: 1 + 3 = 4, 3 + 5 = 8, etc.

(b) The sum of any two even numbers is also an even number.

Example: 2 + 4 = 6, 6 + 8 = 14, etc.

Question 2.

State whether the following statements are true or false:

(a) The sum of three odd numbers is even.

(b) The sum of two odd numbers and one even number is even.

(c) The product of three odd numbers is odd.

(d) If an even number is divided by 2, the quotient is always odd.

(e) All prime numbers are odd.

(f) Prime numbers do not have any factors.

(g) Sum of two prime numbers is always even.

(h) 2 is the only even prime number.

(i) All even numbers are composite numbers.

(j) The product of two even numbers is always even.

Answer:

(a) False.

The sum of three odd numbers is always odd.

Example: 1 + 3 + 5 = 9

(b) True.

The sum of two odd numbers and one even number is even.

Example: 1 + 3 + 2 = 6

(c) True.

The product of three odd numbers is always odd.

Example: 3 * 5 * 7 = 15 * 7 = 105

(d) False.

If an even number is divided by 2, the quotient is always even.

Example: 4/2 = 2

(e) False.

All prime numbers are not odd.

Example: 2 is an even and also a prime number.

(f) False.

All prime numbers have factors 1 and the number itself.

(g) False.

The sum of two prime numbers is either even or odd

Example: 2 + 3 = 5

(h) True.

2 is the only even prime number.

(i)  False

All even numbers are not composite numbers.

Example: 2 is even but not a composite number.

(j) True.

The product of two even numbers is always even.

Example: 2 * 4 = 8

Question 3.

The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to 100.

 

Answer:

The pairs of prime numbers which have the same digits are:

17 and 71; 37 and 73; 79 and 97

So, there are 3 pairs of such prime numbers up to 100.

Question 4.

Write down separately the prime and composite numbers less than 20.

 

Answer:

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19

Composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

Question 5:

What is the greatest prime number between 1 and 10?

Answer:

The prime numbers between 1 and 10 are:

2, 3, 5, 7

Among them, 7 is the greatest numbers.

So, the greatest prime number between 1 and 10 is 7

Question 6:

Express the following as the sum of two odd numbers:

(a) 44   (b) 36   (c) 24   (d) 18

 

Answer 6:

(a) 3 + 41 = 44

(b) 5 + 31 = 36

(c) 7 + 17 = 24

(d) 7 + 11 = 18

Question 7.

Give three pairs of prime numbers whose difference is 2. [Two prime numbers whose difference is 2 are called twin primes.]

 

 Answer:

The three pairs of prime numbers whose difference is 2 are:

 3 and 5;     5 and 7;     11 and 13

Question 8.

Which of the following numbers are prime:

(a) 23   (b) 51   (c) 37   (d) 26

 

Answer:

(a) 23 = 1 * 23

(b) 51 = 3 * 17

(c) 37 = 1 * 37

(d) 26 = 2 * 13

So, (a) 23 and (c) 37 are prime numbers.

Question 9.

Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

 

Answer:

Consecutive composite numbers less than 100 so that there is no prime number between

them, are: 

90, 91, 92, 93, 94, 95, 96

Question 10.

Express each of the following numbers as the sum of three odd primes:

 (a) 21   (b) 31   (c) 53   (d) 61

 

Answer:

(a) 21 = 3 + 7 + 11

(b) 31 = 3 + 11 + 17

(c) 53 = 13 + 17 + 23

(d) 61 = 19 + 29 + 13

Question 11.

Write five pairs of prime numbers less than 20 whose sum is divisible by 5. [Hint: 3 + 7 = 10]

 

Answer:

Five pairs of prime numbers less than 20, whose sum is divisible by 5, are:

2 + 3 = 5

7 + 13 = 20

3 + 17 = 20

2 + 13 = 15

5 + 5 = 10

Question 12.

Fill in the blanks:

(a) A number which has only two factors is called a _______________.

(b) A number which has more than two factors is called a _______________.

(c) 1 neither _______________ nor _______________.

(d) The smallest prime number is _______________.

(e) The smallest composite number is _______________.

(f) The smallest even number is _______________.

 

Answer:

(a) A number which has only two factors is called a prime number.

Example: 2 = 2 * 1

Since it has only two factors 1 and 2, So it is a prime number.

(b) A number which has more than two factors is called a composite number.

Example: 12 = 1 * 12; 12 = 4 * 3; 12 = 6 * 2

Since it has factors 1, 2, 3, 4, 6 and 12, So it is a composite number.

(c) 1 neither prime nor composite.

(d) The smallest prime number is 2.

(e) The smallest composite number is 4.

(f) The smallest even number is 2.

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