Wednesday, 21 March 2012

CBSE Class 6th ( VI) Mathematics Chapter 3. Playing with Numbers: Exercise 3.6

Remember...

  1. The Highest Common Factor (HCF) of two or more given numbers is the highest (or
    greatest) of their common factors. It is also known as Greatest Common Divisor (GCD).
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
218
39
33
1

248
224
212
26
33
1
Factor of 18 = 2 ×3 ×3
Factor of 48 = 2 ×2 × 2× 2× 3
Common Factors of 18 and 48 are = 2 , 3
Highest Common Factor of 18 and 48 is = 2 × 3 = 6
(b)30, 42

230
315
55
1

242
321
77
1
Factor of 30 = 2 ×3 ×5
Factor of 42 = 2 ×3 ×7
Common Factors of 30 and 42 are = 2 , 3
Highest Common Factor of 30 and 42 is = 2 × 3 = 6
(c)18, 60

218
39
33
1

260
230
315
55
1
Factor of 18 = 2 ×3 ×3
Factor of 60 = 2 ×2 ×3×5
Common Factors of 18 and 60 are = 2 , 3
Highest Common Factor of 18 and 60 is = 2 × 3 = 6
(d)27, 63

327
39
33
1

363
321
77
1
Factor of 27 = 3 ×3 ×3
Factor of 63 = 3 ×3 ×7
Common Factors of 27 and 63 are = 3 ,3
Highest Common Factor of 18 and 60 is = 3×3 =9
(e)36, 84

236
218
39
33
1

284
242
321
77
1
Factor of 36 = 2 ×2 ×3 ×3
Factor of 84 = 2 ×2×3 ×7
Common Factors of 36 and 84 are =2 , 2, 3
Highest Common Factor of 36 and 84 is =2 × 2 × 3=12
(f)34, 102

234
1717
1

2102
351
1717
1
Factor of 34 = 2 ×17
Factor of 102 = 2 ×3 ×17
Common Factors of 34 and 60 are =2 , 17
Highest Common Factor of 34 and 60 is =2 ×17 =34

(g)70, 105, 175

270
535
77
1

3105
535
77
1

5175
535
77
1
Factor of 70 = 2 ×5 ×7
Factor of 105 = 3 ×5 ×7
Factor of 175 = 5 × 5 × 7
Common Factors of 70, 105 and 175 are =5,7
Highest Common Factor of 70, 105 and 175 is =5 × 7 =35

(h)91, 112, 49

791
1313
1

2112
256
228
214
77
1

749
77
1
Factor of 91 = 7 ×13
Factor of 112 = 2 ×2 ×2 ×2×7
Factor of 49 = 7 × 7
Common Factors of 91, 112and 49 is 7
Highest Common Factor of 91, 112and 49 is 7

(i)18, 54, 81

218
39
33
1

254
327
39
33
1

381
327
39
33
1
Factor of 18 = 2 ×3 ×3
Factor of 54 = 2 ×3 ×3 ×3
Factor of 81 = 3 × 3× 3× 3
Common Factors of 18, 54and 81 are =3,3
Highest Common Factor of 18, 54and 81 is =3 ×3 =9
(j)12, 45, 75

212
26
33
1

345
315
55
1

375
525
55
1
Factor of 12 = 2 ×2 ×3
Factor of 45 = 3 ×3 ×5
Factor of 75 =3 × 5× 5
Common Factor of 12, 45and 75 is 3
Highest Common Factor of 12, 45and 75 are is 3

2. What is the HCF of two consecutive
(a) numbers? (b) even numbers? (c) odd numbers?

Answer:
(a) Two consecutive Numbers 17,18
HCF of these Two consecutive Numbers 17,18 is as follows:

1717
1

218
39
33
1
Factor of 17 = 1 ×17
Factor of 18 = 1 ×2 ×3 ×3
Clearly Common Factors of 17 and 18 is Just 1
Therefor the Highest Common Factor of 17 and 18 is 1
(a) Two consecutive even numbers 12,14
HCF of these Two consecutive even numbers 12,14 is as follows:

212
26
33
1

214
77
1
Factor of 12 =  ×2 ×2 ×3
Factor of 14 =  ×2 ×7
Clearly Common Factors of 12 and 14 is= 1,2
Therefor the Highest Common Factor of 12 and 14 is =1 ×2 =2
(a) Two consecutive odd numbers 11,13
HCF of these Two consecutive odd numbers 11,13 is as follows:

1111
11
1

1313
11
1
Factor of 11 =  1 , 11
Factor of 13 = 1 , 13
Clearly Common Factors of 11 and 13 is 1
Therefor the Highest Common Factor of 12 and 14 is 1

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

Answer:
Given co-prime numbers are 4, 15 and their respective factorisation
is as given below

24
22
11
1

315
55
11
1
Factor of   4 = 1 × 2 × 2
Factor of 15 = × 3 ×5
Clearly, Common Factors of 4 and 15 is just 1
Since there is no common prime factor except 1,therefor Highest
Common Factors of 4 and 15 is 1


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