## MP Board Class 6th Maths Solutions Chapter 3 Playing With Numbers Ex 3.4

The factors of 84 are 1, 2, 3, 6, 7, 14, 21, and 42.

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) Factors of 20 are 1, 2, 4, 5, 10 and 20

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

∴ Common factors of 20 and 28 are 1, 2 and 4

(b) Factors of 15 are 1, 3, 5 and 15

Factors of 25 are 1, 5 and 25

∴ Common factors of 15 and 25 are 1 and 5

(c) Factors of 35 are 1, 5, 7 and 35

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

∴ Common factors of 35 and 50 are 1 and 5

(d) Factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56

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

∴ Common factors of 56 and 120 are 1, 2, 4 and 8

What is the greatest common factor of 12 and 18 ? 6.

Question 2.

Find the common factors of:

(a) 4, 8 and 12

(b) 5,15 and 25

Solution:

(a) Factors of 4 are 1, 2 and 4 Factors of 8 are 1, 2, 4 and 8 Factors of 12 are 1, 2, 3, 4, 6 and 12

∴ Common factors of 4, 8 and 12 are 1, 2 and 4

(b) Factors of 5 are 1 and 5 Factors of 15 are 1, 3, 5 and 15

Factors of 25 are 1, 5 and 25 .-. Common factors of 5, 15 and 25 are 1 and 5

Find the factors of 18 and 40.

Question 3.

Find first three common multiples of:

(a) 6 and 8

(b) 12 and 18

Solution:

(a) Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72,

Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72,

∴ First three common multiples of 6 and 8 are 24, 48 and 72

(b) Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120,

Multiples of 18 are 18, 36, 54, 72, 90, 108, 126,

∴ First three common multiples of 12 and 18 are 36, 72 and 108

Question 4.

Write ail 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, 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 are 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 which are less than 100 are 12, 24, 36, 48, 60, 72, 84 and 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

Solution:

(a) Factors of 18 are 1, 2, 3, 6, 9 and 18

Factors of 35 are 1, 5, 7 and 35 Common factor of 18 and 35 is 1 Since, both have only one common factor, i.e., 1.

Therefore, 18 and 35 are co-prime numbers.

(b) Factors of 15 are 1, 3, 5 and 15

Factors of 37 are 1 and 37 Common factor of 15 and 37 is 1

Since, both have only one common factor, i.e., 1. Therefore, 15 and 37 are co-prime numbers.

(c) Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30

Factors of 415 are 1, 5, , 83 and 415

Common factors of 30 and 415 are 1 and 5

Since, both have more than one common factor. Therefore, 30 and 415 are not co-prime numbers.

(d) Factors of 17 are 1 and 17

Factors of 68 are 1, 2, 4, 17, 34 and 68 Common factors of 17 and 68 are 1 and 17

Since, both have more than one common factor. Therefore, 17 and 68 are not co-prime numbers.

(e) Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216

Factors of 215 are 1, 5, 43 and 215 Common factor of 216 and 215 is 1 Since, both have only one common factor, i.c., 1. Therefore, 216 and 215 are co-prime numbers.

(f) Factors of 81 are 1, 3, 9, 27 and 81 Factors of 16 are 1, 2, 4, 8 and 16 Common factor of 81 and 16 is 1 Since, both have only one common factor, i.e., 1. Therefore, 81 and 16 are co-prime numbers.

The prime factors of 50 are the prime numbers which divide 50 exactly, without remainder as defined by the Euclidean division.

Question 6.

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

Solution:

Since 5 × 12 = 60. The number divisible by both 5 and 12, must also be divisible by 60.

Question 7.

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

Solution:

Factors of 12 are 1, 2, 3, 4, 6 and 12.

Therefore, the number divisible by 12, will also be divisible by 1, 2, 3, 4 and 6.