NCERT Exercise 3.4 Solution class six math
Question (1) Find the common factors of:
(a) 20 and 28
Solution
The factors of 20 = 1, 2, 4, 5, 10, and 20
And the factors of 28 = 1, 2, 4, 7, 14, and 28
Thus, common factors of 20 and 28 = 1, 2, and 4 Answer
(b) 15 and 25
Solution
The factors of 15 = 1, 3, 5, and 15
The factors of 25 = 1, 5, and 25
Thus common factors of 15 and 25 = 1 and 5 Answer
(c) 35 and 50
Solution
The factors of 35 = 1, 5, 7, and 35
The factors of 50 = 1, 2, 5, 10, 25, and 50
Thus common factors of 35 and 50 = 1 and 5 Answer
(d) 56 and 120
Solution
The factors of 56 = 1, 2, 4, 7, 8, and 56
The factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, 60, and 120
Thus the common factors of 56 and 120 = 1, 2, 4, and 8 Answer
Question (2) Find the common factors of:
(a) 4, 8 and 12
Solution
The factors of 4 = 1, 2, and 4The factors of 8 = 1, 2, 4, and 8
The factors of 12 = 1, 2, 3, 4, 6, and 12
Thus common factors of 4, 8 and 12 = 1, 2, and 4 Answer
(b) 5, 15 and 25
Solution
The factors of 5 = 1 and 5
The factors of 15 = 1, 3, 5, and 15
The factors of 25 = 1, 5, and 25
Thus common factors of 5, 15 and 25 = 1 and 5 Answer
Question (3) Find the first three common multiples of:
(a) 6 and 8
Solution
The multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78. . .
The multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . .
Thus, first three common multiples of 6 and 8 = 24, 48 and 72 Answer
(b) 12 and 18
Solution
The multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, . . .
The multiples of 18 = 18, 36, 54, 72, 90, 108, 126, . . .
Thus the first three common multiples of 12 and 18 = 36, 72, and 108 Answer
Question (4) Write all the numbers less than 100 which are common multiples of 3 and 4
Solution
The multiples of 3 which are less than 100
= 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, and 96
The multiples of 4 which are less than 100
= 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, and 96
Thus, all the numbers less than 100 and common multiples of 3 and 4
= 12, 24, 36, 48, 60, 72, 84, and 96 Answer
Question (5) Which of the following numbers are co-prime
(a) 18 and 35
Answer: 18 and 35 are co-prime
Solution
The factors of 18 = 1, 2, 3, 6, 9, and 18
The factors of 35 = 1, 5, 7, and 35
The common factors of 18 and 35 = 1
Since the common factors of 18 and 35 = 1, thus 18 and 35 are co-prime
(b) 15 and 37
Answer: 15 and 37 are co-prime
Explanation
The factors of 15 = 1, 3, 5, and 15
The factors of 37 = 1, and 37 (37 is a prime number)
The common factors of 15 and 37 = 1
Since the common factors of 15 and 37 = 1, thus 15 and 37 are co-prime
(c) 30 and 415
Answer: 30 and 415 are not co-prime
Explanation
The factors of 30 = 1, 2, 3, 5, 6, 15, and 30
The factors of 415 = 1, 5, 83, and 415
The common factors of 415 = 1 and 5
Since 30 and 415 has two common factors 1 and 5, thus 30 and 415 are not co-prime
(d) 17 and 68
Answer 17 and 68 are not co-prime
Explanation
The factors of 17 = 1 and 17 (17 is a prime number)
The factors of 68 = 1, 4, 17, and 68
The common factors of 17 and 68 = 1 and 17
Since 17 and 68 has two common factors 1 and 17, thus 17 and 68 are not co-prime
(e) 216 and 215
Answer: 216 and 215 are co-prime
Explanation
The factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216
The factors of 215 = 1, 5, 43, and 215
The common factors of 216 and 215 = 1
Since, 216 and 215 has common factors = 1, thus 216 and 215 are co-prime
(f) 81 and 16
Answer 81 and 16 are co-prime
Explanation
The factors of 81 = 1, 3, 9, 27, and 81
The factors of 16 = 1, 2, 4, 8, and 16
Thus the common factors of 81 and 16 = 1
Since there is no common factor other than 1 between 81 and 16, thus 81 and 16 are co-prime
Question (6) A number is divisible by both 5 and 12. By which other number will that number be always divisible?
Answer Number which is divisible by 5 and 12 both will be always divisible by the factors of 5 and 12.
Explanation
The factors of 5 = 1 and 5 (5 is a prime number)
The factors of 12 = 1, 2, 3, 4, 6, and 12
Since, there is no common factor other than 1 between 5 and 12, thus 5 and 12 are co-prime.
Thus, smallest number which is divisible by both 5 and 12 = 5 × 12 = 60
Now, since 12 is one of the multiple of 60, thus 60 is divisible by 1, 2, 3, 4, and 6 other than 5 and 12
Question (7) A number is divisible by 12. By what other numbers will that number be divisible?
Answer Number which is divisible by 12 will be divisible by all factors of 12 also.
The factors of 12 = 1, 2, 3, 4, 6, and 12
Thus, the number which is divisible by 12 will be divisible by 1, 2, 3, 4, and 6 also.