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Questions and Solutions for NCERT Class 6th Mathematics Chapter 3 – Playing with Numbers – Exercise 3.4
1. Find the common factors of :
(a) 20 and 28
Sol: 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
Sol: Factors of 15 are 1, 3, 5, 15
factors of 25 are 1, 5, 25
Common factors of 15 and 25 are 1, 5
(c) 35 and 50
Sol: Factors of 35 are 1, 5, 7, 35
Factors of 50 are 1, 2, 5, 10, 25, 50
Common factors of 35 and 50 are 1 ,5
(d) 56 and 120
Sol: Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 60, 120
Common factors of 56 and 120 are 1, 2, 4, 8
2. Find the common factors of :
(a) 4, 8 and 12
Sol: 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, 12 are 1, 2, 4
(b) 5, 15 and 25
Factors of 5 are 1, 5
Factors of 15 are 1, 3, 5, 15
Factors of 25 are 1, 5, 25
Common Factors of 5, 15, 25 are 1, 5
3. Find first three common multiples of :
(a) 6 and 8
Sol: Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78 _ _ _ _
Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 _ _ _ _
First three Common Multiple of 6 and 8 are 24, 48 and 72
(b) 12 and 18
Sol: Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144 _ _ _ _
Multiples of 18 are 18, 36, 54, 72, 90, 108, 126, 144, _ _ _ _
First three common multiples of 12 and 18 are 36, 72 and 108
4. Write all the numbers less than 100 which are common multiples of 3 and 4.
Sol: Multiples of 3 are 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 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96
Common multiples of 3 and 4, which are less than 100 are 12, 24, 36, 48, 60, 72, 84. 96
5. Which of the following numbers are co-prime?
(a) 18 and 35
Sol: Factors of 18 are 1, 2, 3, 6, 9, 18
Factors of 35 are 1, 5, 7, 35
Since, common factor of 18 and 35 is 1, they are co-prime numbers
(b) 15 and 37
Sol: Factors of 15 are 1, 3, 5, 15
Factors of 37 are 1, 37
Since common factor of 15 and 37 is 1, they are co-prime numbers
(c) 30 and 415
Sol: Factors of 30 are 1, 2, 3, 5, 6, 15, 30
Factors of are 415 are 1, 5, 83, 415
Since common factors of 30 and 415 are 1 and 5 , they are not co-prime numbers
(d) 17 and 68
Sol: Factors of 17 are 1, 17
Factors of 68 are 1, 2, 4, 17, 34, 68
Since common factors of 17 and 68 are 1 and 17 , they are not co-prime numbers
(e) 216 and 215
Sol: Factors of 216 are 1, 2, 3, 4, 6, 8, 36, 72, 108, 216
Factors of 215 are 1, 5, 43, 215
Since common factors of 216 and 215 is 1 , they are co-prime numbers
(f) 81 and 16
Sol: Factors of are 1, 3, 9, 27, 81
Factors of are 1, 2, 4, 8, 16
Since common factor of 81 and 16 is 1 , they are co-prime numbers
6. A number is divisible by both 5 and 12. By which other number will that number be always divisible?
Ans: If the number is divisible by both 5 and 12 then it will be divisible by product of 5 and 15 i.e. 60
7. A number is divisible by 12. By what other numbers will that number be divisible?
Ans: Factors of 12 are 1, 2, 3, 4, 6 and 12
Therefore the number should also be divisible by 1, 2, 3, 4 and 6
You can find the solutions for Class 6 Mathematics previous exercises from here
- Playing with Numbers – Exercise 3.3 Solutions
- Playing with Numbers – Exercise 3.2 Solutions
- Playing with Numbers – Exercise 3.1 Solutions
- Whole Numbers – Exercise 2.3 Solutions
- Whole Numbers – Exercise 2.2 Solutions
- Whole Numbers – Exercise 2.1 Solutions
- Knowing Our Numbers Solutions Exercise 1.3 Solutions
- Knowing Our Numbers Solutions Exercise 1.2 Solutions
- Knowing Our Numbers Solutions Exercise 1.1 Solutions
