## 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 4**

The 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.