Playing with Numbers-Solutions Ex. 3.4
CBSE Class –VI Mathematics
NCERT Solutions
Chapter 3 Playing With Numbers (Ex. 3.4)
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
(b) 15 and 25
(c) 35 and 50
(d) 56 and 120
Answer:
(a) Factors of 20 = 1, 2, 4, 5, 10, 20
Factors of 28 = 1, 2, 4, 7, 14, 28
Common factors = 1, 2, 4
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
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
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
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
(b) 5, 15 and 25
Answer:
(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
(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
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
(b) 12 and 18
Answer:
(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
(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
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
(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.
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.
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.
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.
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.
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.
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.
Therefore, the number also be divisible by 1,2 ,3, 4 and 6.
