### 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

(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.