Exercise 3.6 - Chapter 3 - Playing with numbers - Ncert Solutions class 6 - Maths
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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
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.
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.
