NCERT Solutions for Class 6 Mathematics Chapter 3 Playing with Numbers Exercise 3.6

Exercise 3.6

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Ex-3.1
Ex-3.2
Ex-3.3
Ex-3.4
Ex-3.5
Ex-3.6
Ex-3.7

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Q 1 - Ex 3.6 - Playing With Numbers - NCERT Maths Class 6th - Chapter 3

Page No 63:

Question 1:

Find the HCF of the following numbers:
(a) 18, 48 (b) 30, 42 (c) 18, 60
(d) 27, 63 (e) 36, 84 (f) 34, 102
(g) 70, 105, 175 (h) 91, 112, 49 (i) 18, 54, 81
(j) 12, 45, 75

Answer:

(a) 18, 48

2	18
3	9
3	3
	1

2	48
2	24
2	12
2	6
3	3
	1

18 = 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
HCF = 2 × 3 = 6
(b) 30, 42

2	30
3	15
5	5
	1

2	42
3	21
7	7
	1

30 = 2 × 3 × 5
42 = 2 × 3 × 7
HCF = 2 × 3 = 6
(c) 18, 60

2	18
3	9
3	3
	1

2	60
2	30
3	15
5	5
	1

18 = 2 × 3 × 3
60 = 2 × 2 × 3 × 5
HCF = 2 × 3 = 6
(d) 27, 63

3	27
3	9
3	3
	1

3	63
3	21
7	7
	1

27 = 3 × 3 × 3
63 = 3 × 3 × 7
HCF = 3 × 3 = 9
(e) 36, 84

2	36
2	18
3	9
3	3
	1

2	84
2	42
3	21
7	7
	1

36 = 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
HCF = 2 × 2 × 3 = 12
(f) 34, 102

2	34
17	17
	1

2	102
3	51
17	17
	1

34 = 2 × 17
102 = 2 × 3 × 17
HCF = 2 ×17 = 34
(g) 70, 105, 175

2	70
5	35
7	7
	1

3	105
5	35
7	7
	1

5	175
5	35
7	7
	1

70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
HCF = 5 × 7 = 35
(h) 91, 112, 49

7	91
13	13
	1

2	112
2	56
2	28
2	14
7	7
	1

7	49
7	7
	1

91 = 7 × 13
112 = 2 × 2 × 2 × 2 × 7
49 = 7 × 7
HCF = 7
(i) 18, 54, 81

2	18
3	9
3	3
	1

2	54
3	27
3	9
3	3
	1

3	81
3	27
3	9
3	3
	1

18 = 2 × 3 × 3
54 = 2 × 3 × 3 × 3
81 = 3 × 3 × 3 × 3
HCF = 3 × 3 = 9
(j) 12, 45, 75

2	12
2	6
3	3
	1

3	45
3	15
5	5
	1

3	75
5	25
5	5
	1

12 = 2 ×2 × 3
45 = 3 × 3 × 5
75 = 3 × 5 × 5
HCF = 3

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Q 2 - Ex 3.6 - Playing With Numbers - NCERT Maths Class 6th - Chapter 3

Question 2:

What is the HCF of two consecutive
(a) Numbers? (b) Even numbers? (c) Odd numbers?

Answer:

(i) 1 e.g., HCF of 2 and 3 is 1.
(ii) 2 e.g., HCF of 2 and 4 is 2.
(iii) 1 e.g., HCF of 3 and 5 is 1.

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Q 3 - Ex 3.6 - Playing With Numbers - NCERT Maths Class 6th - Chapter 3

Page No 64:

Question 3:

HCF of co-prime numbers 4 and 15 was found as follows by factorization:
4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factors, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF?

Answer:

No. The answer is not correct. 1 is the correct HCF.