### Playing with Numbers-Solutions Ex. 3.4

CBSE Class –VI Mathematics
NCERT Solutions
Chapter 3 Playing With Numbers (Ex. 3.4)

Question 1. Find the common factors of:
(a) 20 and 28
(b) 15 and 25
(c) 35 and 50
(d) 56 and 120
(a) Factors of 20 = 1, 2, 4, 5, 10, 20
Factors of 28 = 1, 2, 4, 7, 14, 28
Common factors = 1, 2, 4
(b) Factors of 15 = 1, 3, 5, 15
Factors of 25 = 1, 5, 25
Common factors = 1, 5
(c) Factors of 35 = 1, 5, 7, 35
Factors of 50 = 1, 2, 5, 10, 25, 50
Common factors = 1, 5
(d) 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
(b) 5, 15 and 25
(a) 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 = 1, 2, 4
(b) Factors of 5 = 1, 5
Factors of 15 = 1, 3, 5, 15
Factors of 25 = 1, 5, 25
Common factors of 5, 15 and 25 = 1, 5
Question 3. Find the first three common multiples of:
(a) 6 and 8
(b) 12 and 18
(a) 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, …………………….
Common multiples of 6 and 8 = 24, 48, 72
(b) Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ………
Multiples of 18 = 18, 36, 54, 72, 90, 108, ………………………………
Common multiples of 12 and 18 = 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 = 12, 24, 36, 48, 60, 72, 84, 96
Question 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) Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 35 = 1, 5, 7, 35
Common factor = 1
Since, both numbers have only one common factor, i.e., 1, therefore, they are co-prime numbers.
(b) Factors of 15 = 1, 3, 5, 15
Factors of 37 = 1, 37
Common factor = 1
Since, both numbers have only one common factor, i.e., 1, therefore, they are co-prime numbers.
(c) Factors of 30 = 1, 2, 3, 5, 6, 15, 30
Factors of 415 = 1, 5, …….., 83, 415
Common factors = 1, 5
Since, both numbers have more than one common factors, therefore, they are not co-prime numbers.
(d) Factors of 17 = 1, 17
Factors of 68 = 1, 2, 4, 17, 34, 86
Common factors = 1, 17
Since, both numbers have more than one common factors, therefore, they are not co-prime numbers.
(e) Factors of 216 = 1, 2, 3, 4, 6, 8, 36, 72, 108, 216
Factors of 215 = 1, 5, 43, 215
Common factor = 1
Since, both numbers have only one common factor, i.e., 1, therefore, they are co-prime numbers.
(f) Factors of 81 = 1, 3, 9, 27, 81
Factors of 16 = 1, 2, 4, 8, 16
Common factor = 1
Since, both numbers 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 other number will that number be always divisible?
Answer: 5 x 12 = 60. The number must be divisible by 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, 12.
Therefore, the number also be divisible by 1,2 ,3, 4 and 6.