Chapter - 3 Playing with Numbers

Q&A -Ask Doubts and Get Answers

Q
Playing With Numbers

Question:

1. Find the common factors of :

(a) 20 and 28      (b) 15 and 25     (c) 35 and 50     (d) 56 and 120 

Solution: (a) 20 and 28

Factors of 20: 1, 2, 4, 5, 10 and 20

Factors of 28: 1, 2, 4, 7, 14 and 28

Common factors = 1, 2, 4

(b) 15 and 25

Factors of 15: 1, 3, 5 and 15

Factors of 25: 1, 5 and 25

Common factors = 1, 5

(c) 35 and 50

Factors of 35: 1, 5, 7 and 35

Factors of 50: 1, 2, 5, 10, 25 and 50

Common factors = 1, 5

(d) 56 and 120

Factors of 56: 1, 2, 4, 7, 8, 14, 28 and 56

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120

Common factors = 1, 2, 4, 8

 

2. Find the common factors of :

(a) 4, 8 and 12          (b) 5, 15 and 25

Solution: (a) 4, 8 and 12

Factors of 4: 1, 2 and 4

Factors of 8: 1, 2, 4 and 8

Factors of 12: 1, 2, 3, 4, 6 and 12

Common factors = 1, 2, 4

(b) 5, 15 and 25

Factors of 5: 1 and 5

Factors of 15: 1, 3, 5 and 15

Factors of 25: 1. 5 and 25

Common factors = 1, 5

 

3. Find first three common multiples of :

(a) 6 and 8         (b) 12 and 18 

Solution: (a) 6 and 8  

Multiple of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72 are multiples of 6.

Multiple of 8: 8, 16, 24, 32, 40, 48, 56, 72 are multiples of 8.

Three common multiples are 24, 48 and 72.

(b) 12 and 18

Multiple of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108 are multiples of 12

Multiple of 18: 18, 36, 54, 72, 90, 108 are multiples of 18

Three common factors are 36, 72 and 108.

 

4. Write all the numbers less than 100 which are common multiples of 3 and 4.

Solution: Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24 ...

Multiples of 4 are 4, 8, 12, 16, 20, 24...

The first two common multiples of 3 and 4 are 12, 24 which are multiple of 12.

So, all common multiples of 4 and 3 are multiple of 12.

Therefore, common multiples of 3 and 4 less than 100 are 12, 24, 36, 48, 60, 72. 84 and 96.

 

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

Solution: (a) 18 and 35

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 35: 1, 5, 7, 35

Common factor = 1

Since, their common factor is 1. Hence, the given two numbers are co-prime.

(b) 15 and 37

Factors of 15: 1, 3, 5, 15

Factors of 37: 1, 37

Common factors = 1

Since, their common factor is I. Hence, the given two numbers are co-prime.

(c) 30 and 415

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 415: 1, 5, 83, 415

Common factors = 1, 5

Since, their common factor is not only 1. Hence, the given two numbers are not co-prime.

(d) 17 and 68

Factors of 17: 1, 17

Factors of 68: 1, 2, 4, 17, 34, 68

Common factors = 1, 17

Since, their common factor is not only 1. Hence, the given two numbers are not co-prime.

(e) 216 and 215

Factors of 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

Factors of 215: 1, 5, 43, 215

Common factors = 1

Since, their common factor is 1. Hence, the given two numbers are co-prime.

(f) 81 and 16

Factors of 81: 1, 3, 9, 27, 81

Factors of 16: 1, 2, 4, 8, 16

Common factors = 1

Since, their common factor is 1. Hence, the given two numbers are co-prime.

 

6. A number is divisible by both 5 and 12. By which other number will that number be always divisible?

Solution: The number is divisible by both 5 and 12, so the number will also be divisible by the product of 5 and 12.

5 x 12 = 60.

Therefore, the number always be divisible by 60.

 

7. A number is divisible by 12. By what other numbers will that number be divisible?

Solution: Factors of 12: 1, 2, 3, 4, 6 and 12.

So, the number also be divisible with 1, 2, 3, 4 and 6.

Answer:


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