RBSE Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.4

Rajasthan Board RBSE Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.4 Textbook Exercise Questions and Answers.

RBSE Class 6 Maths Solutions Chapter 3 Playing With Numbers Ex 3.4

Question 1.
Find the common factors of:
(a) 20 and 28
Answer:
20 and 28
Factors of 20 = 1, 2, 4, 5,10, 20
Factors of 28 = 1, 2, 4, 7,14, 28
Common factors = 1, 2,4

(b) 15 and 25
Answer:
15 and 25
Factors of 15- = 1, 3, 5,15
Factors of 25 = 1, 5, 25
Common factors = 1, 5

(c) 35 and 50
Answer:
35 and 50
Factors of 35 = 1, 5, 7, 35
Factors of 50 = 1,2,5,10, 25, 50
Common factors = 1,5

(d) 56 and 120
Answer:
56 and 120
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 60, 120
Common factors = 1, 2,4, 8

Question 2.
Find the common factors of:
(a) 4, 8 and 12
Answer:
4, 8 and 12
Factors of 4 = 1, 2,4
Factors of 8 = 1, 2,4, 8
Factors of 12 = 1, 2, 3, 4, 6,12
Common factors of 4,8, and 12 are 1,2,4.

(b) 5, 15 and 25
Answer:
5,15 and 25
Factors of 5 = 1, 5
Factors of 15 = 1, 3, 5,15
Factors of 25 = 1, 5, 25
Common factors of 5,15, 25 are 1, 5.

Question 3.
Find first three common multiples of:
(a) 6 and 8
Answer:
6 and 8
Multiples of 6 = 6,12,18,24,30,36,42, 48, 54, 60, 72 ...
Multiples of 8 = 8,16,24,32,40,48,56, 64, 72, 80,...
First three common multiples of 6 and 8 are 24,48, 72.

(b) 12 and 18
Answer:
12 and 18
Multiples of 12 = 12,24, 36,48,60,72, 84,96,108,...
Multiples of 18 = 18,36,54,72,90,108, 126,...
First three common multiples of 12 and 18 are 36,72,108.

Question 4.
Write all the numbers less than 100 which are common multiples of 3 and 4.
Answer:
Multiples of 3 = 3, 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, 93, 96,99.
Multiples of 4 = 4, 8,12,16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96,100.
Common multiples of 3 and 4 are 12,24,36, 48, 60, 72, 84,96.

Question 5.
Which of the following numbers are co-prime?
(a) 18 and 35
Answer:
18 and 35
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 35 = 1, 5, 7, 35
Common factors = 1
Since, both have only one common factor, i.e. 1, therefore, they are co-prime numbers.

(b) 15 and 37
Answer:
15 and 37
Factors of 15 = 1, 3, 5,15
Factors of 37 = 1, 37
Common factors = 1
Since, both have only one common factor, i.e. 1, therefore, they are co-prime numbers.

(c) 30 and 415
Answer:
30 and 415
Factors of 30 = 1, 2, 3, 5, 6, 15, 30
Factors of 415 = 1, 5, 82,415
Common factors =1,5
Since, both have more than one common factor, therefore they are not co-prime numbers.

(d) 17 and 68
Answer:
17 and 68
Factors of 17 = 1,17
Factors of 68 = 1, 2, 4, 17, 34, 68
Common factors = 1,17
Since, both have more than one common factor, therefore they are not co-prime numbers.

(e) 216 and 215
Answer:
216 and 215
Factors of 216 = 1, 2, 3, 4, 6, 9, 36, 72, 108, 216
Factors of 215= 1, 5, 43, 215
Common factors = 1
Since, both have only one common factor, i.e. 1 therefore, they are co-prime numbers.

(f) 81 and 16
Answer:
81 and 16
Factors of 81 = 1, 3, 9, 27, 81
Factors of 16 = 1, 2,4, 8,16
Common factors = 1
Since, both have only one common . factor, i.e. 1 therefore, they are co-prime numbers.

Question 6.
A number is divisible by both 5 and 12. By which other1 number will that number be always divisible?
Answer:
Factors of 5 = 1, 5
Factors of 12 = 1, 2, 3, 4,6,12
As the common factor of these number is 1, the given two numbers are co-prime and the number will also be divisible by their product, i.e. 5 × 12 = 60
So, the factors of 60 are : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Question 7.
A number is divisible by 12. By what other numbers will that number be divisible?
Answer:
Factors of 12 are: 1,2,3,4,6 and 12. Since, the number is divisible by 12. So, it will also be divisible by all its factors, i.e. 1, 2, 3,4, 6,12.
Clearly, 1, 2, 3, 4, 6 are the numbers other than 12 by which this number is also divisible.