Tuesday, 13 March 2012

CBSE Class 6th ( VI) Mathematics Chapter 3. Playing with Numbers :Exercise 3.4


1. Find the common factors of :
(a) 20 and 28 (b) 15 and 25 (c) 35 and 50 (d) 56 and 120


Answer:
(a) 20 and 28
Factors of 20 are:1, 2, 4, 5, 10, 20
Factors of 28 are:1, 2, 4, 7, 14, 28
Common factors of 20 and 28 are 1, 2, 4
(b) 15 and 25
Factors of 15 are: 1, 5, 15
Factors of 25 are:1, 5, 25
Common factors of 15 and 25 are 1, 5
(c) 35 and 50
Factors of 35 are:1, 5, 35
Factors of 50 are:1, 5, 10, 50
Common factors of 35 and 50 are 1, 5
(d) 56 and 120
Factors of 56 are:1, 2, 4, 8, 56
Factors of 120 are:1, 2, 4, 5, 6, 8, 60, 120
Common factors of 56 and 120 are 1, 2, 4, 8,

2. Find the common factors of :
(a) 4, 8 and 12 (b) 5, 15 and 25


Answer:
(a) 4, 8 and 12
Factors of 4 are:1, 2, 4
Factors of 8 are:1, 2, 4, 8
Factors of 12 are:1, 2, 3, 4, 6, 12
Common factors of 4, 8 and 12 are 1, 2, 4
(b) 5, 15 and 25
Factors of 5 are: 1, 5
Factors of 15 are:1, 5, 15
Factors of 25 are:1, 5, 25
Common factors of 5, 15 and 25 are 1, 5
3. Find first three common multiples of :
(a) 6 and 8 (b) 12 and 18


Answer:
(a) 6 and 8
multiples of 6 are:6, 12, 18, 24, 30, 36, 42, 48, 54, 60
multiples of 8 are:8, 16, 24, 32, 40, 48, 56, 64, 72, 180
Common multiples of 6 and 8 are: 24, 48, 72
(b) 12 and 18
multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
multiples of 18 are:18, 36, 54, 72, 90, 108, 126, 144, 162, 180
Common multiples of 12 and 18 are 36, 72, 108
4. Write all the numbers less than 100 which are common multiples of 3 and 4.

Answer:
Numbers less than 100 which are multiples of 3 are3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48,51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 96, 99
Numbers less than 100 which are multiples of 4 are4, 8, 12, 16, 20, 24, 28, 32, 36, 40 , 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96
The numbers less than 100 which are common multiples of 3 and 4 are 12, 24, 36, 48, 60, 72, 84 and 96

5. Which of the following numbers are co-prime?
(a) 18 and 35 (b) 15 and 37 (c) 30 and 415
(d) 17 and 68 (e) 216 and 215 (f) 81 and 16


Answer:

(a) 18 and 35 (c) 30 and 415 (d) 17 and 68 (e) 216 and 215 (f) 81 and 16
We know that Two numbers having only 1 as a common factor are called co-prime numbers.
Factor of 18 are1, 2, 3, 6, 9
Factor of 35 are1, 5, 7
As the common factor of 18 and 35 is just 1, there for 18 and 35 are co-prime numbers
(b) 15 and 37
Factor of 15 are1, 5, 15
Factor of 37 are1, 37
As the common factor of 15 and 37 is just 1, there for 15 and 37 are co-prime numbers
Factor of 30 are1, 2, 3, 5, 6, 10, 15, 30
Factor of 415 are1, 5, 15, 415
As the common factor of 30 and 415  are 1, 5, 15 there for 30 and 415 are not co-prime numbers
Factor of 17 are1,17
Factor of 68 are1, 2, 4, 17
As the common factor of 17 and 68 are 1,17 there for 17 and 68 are not co-prime numbers
Factor of 216 are1, 2, 8, 108, 216
Factor of 215 are1, 5, 15
As the common factor  216 and 215 is just 1,there for  216 and 215 are co-prime numbers
Factor of 81 are1, 3, 9, 27, 81
Factor of 16 are1, 2, 4, 8
As the common factor 81 and 16 is just 1, there for 81 and 16 are co-prime numbers

6. A number is divisible by both 5 and 12. By which other number will that number be
always divisible?

Answer:
(a) 5 and 12
multiples of 5 are:5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
multiples of 12 are:12, 24, 36, 48, 60
Common multiple of 5 and 12 is 60,hence 60 is that number
60 is divisible by 1, 2, 3, 4, 5, 6, 10, 60



7. A number is divisible by 12. By what other numbers will that number be divisible?

Answer:
Number divisible by 12 are Multples of 12  i.e 12,24,36,48,60,72,84,96,108,120
Out of these posible numbers which are multiples of 12, the numbers will be divisible by every factor of that number
For example here 60 is a multple of 12 thus divisible by 12 and also divisible by its factors like 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60



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