Class-6 Maths Chapter-3 PLAYING WITH NUMBERS

 EVENTS CONVENT HIGH SCHOOL

15/01/2021                        CLASS-6                                  SLOT-2

MATHS

Chapter-3 PLAYING WITH NUMBERS

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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

24 = 1 × 24 24 = 2 × 12 24 = 3 × 8

24 = 4 × 6 24 = 6 × 4

∴Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24

(b) 15

15 = 1 × 15 15 = 3 × 5 15 = 5 × 3

∴Factors of 15 are 1, 3, 5, and 15

(c) 21

21 = 1 × 21 21 = 3 × 7 21 = 7 × 3

∴Factors of 21 are 1, 3, 7, and 21

(d) 27

27 = 1 × 27 27 = 3 × 9 27 = 9 × 3

∴Factors of 27 are 1, 3, 9, and 27

(e) 12

12 = 1 × 12 12 = 2 × 6 12 = 3 × 4 12 = 4 × 3

∴Factors of 12 are 1, 2, 3, 4, 6, and 12

(f) 20

20 = 1 × 20 20 = 2 × 10 20 = 4 × 5 20 = 5 × 4

∴Factors of 20 are 1, 2, 4, 5, 10, and 20

(g) 18

18 = 1 × 18 18 = 2 × 9 18 = 3 × 6 18 = 6 × 3

∴Factors of 18 are 1, 2, 3, 6, 9, and 18

(h) 23

23 = 1 × 23 23 = 23 × 1

∴ Factors of 23 are 1 and 23

(i) 36

36 = 1 × 36 36 = 2 × 18 36 = 3 × 12 36 = 4 × 9

36 = 6 × 6

∴Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36

 

 

Question 2:Write first five multiplies of:(a) 5 (b) 8 (c) 9

Answer:

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

∴ The required multiples are 5, 10, 15, 20, and 25.

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

∴ The required multiples are 8, 16, 24, 32, and 40.

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

∴ The required multiples are 9, 18, 27, 36, and 45.

Question 3:Match the items in column 1 with the items in column 2.

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

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Question 4:Find all the multiples of 9 up to 100.

Answer:

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

Therefore, the multiples of 9 up to 100 are

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

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Question 1:What is the sum of any two (a) Odd numbers? (b) Even numbers?

Answer:

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

e.g., 1 + 3 = 4

13 + 19 = 32

(b) The sum of two even numbers is even.

e.g., 2 + 4 = 6

10 + 18 = 28

Question 2: State whether the following statements are True or False:

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

a.     False 3 + 5 + 7 = 15, i.e., odd

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

a.     True 3 + 5 + 6 = 14, i.e., even

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

a.     True 3 × 5 × 7 = 105, i.e., odd

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

a.     False 4 ÷ 2 = 2, i.e., even

(e)   All prime numbers are odd.

a.     False 2 is a prime number and it is also even

(f)    Prime numbers do not have any factors.

a.     False 1 and the number itself are factors of the number

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

a.     False 2 + 3 = 5, i.e., odd

(h)   2 is the only even prime number.

a.     True

(i)     All even numbers are composite numbers.

a.     False 2 is a prime number

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

a.     True 2 × 4 = 8, i.e., even

 

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:

17, 71

37, 73

79, 97

Question 4:Write down separately the prime and composite numbers less than 20.

Answer:

Prime numbers less than 20 are

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

Composite numbers less than 20 are

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

Question 5:What is the greatest prime number between 1 and 10?

Answer:

Prime numbers between 1 and 10 are 2, 3, 5, and 7. Among these numbers, 7 is the greatest.

Question 6:Express the following as the sum of two odd primes.

(a) 44 (b) 36 (c) 24 (d) 18

Answer:

(a) 44 = 37 + 7

(b) 36 = 31 + 5

(c) 24 = 19 + 5

(d) 18 = 11 + 7

Question 7:Give three pairs of prime numbers whose difference is 2.

[Remark: Two prime numbers whose difference is 2 are called twin primes].

Answer:

3, 5

41, 43

71, 73

Question 8:Which of the following numbers are prime?

(a) 23 (b) 51 (c) 37 (d) 26

Answer:

(a) 23 23 = 1 × 23 23 = 23 × 1

23 has only two factors, 1 and 23. Therefore, it is a prime number.

(b) 51 51 = 1 × 51 51 = 3 × 17

51 has four factors, 1, 3, 17, 51. Therefore, it is not a prime number. It is a composite number.

(c) 37

It has only two factors, 1 and 37. Therefore, it is a prime number.

(d) 26

26 has four factors (1, 2, 13, 26). Therefore, it is not a prime number. It is a composite number.

 

Question 9:Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

Answer:

Between 89 and 97, both of which are prime numbers, there are 7 composite numbers. They are

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

Numbers Factors

90 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

91 1, 7, 13, 91

92 1, 2, 4, 23, 46, 92

93 1, 3, 31, 93

94 1, 2, 47, 94

95 1, 5, 19, 95

96 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

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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 = 5 + 7 + 19

(c) 53 = 3 + 19 + 31

(d) 61 = 11 + 19 + 31

 

Question 11:Write five pairs of prime numbers less than 20 whose sum is divisible by 5.

(Hint: 3 + 7 = 10)

Answer:

2 + 3 = 5

2 + 13 = 15

3 + 17 = 20

7 + 13 = 20

19 + 11 = 30

 

Question 12:Fill in the blanks:

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

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

(c) 1 is neither Prime number, nor  composite number

(d) The smallest prime number is 2

(e) The smallest composite number is  4

(f) The smallest even number is 2