NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4 are the part of NCERT Solutions for Class 6 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4 (Rationalised Contents)

Ex 3.4 Class 6 Maths 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) The given numbers are: 20 and 28
Factors of 20 are 1, 2, 4, 5, 10, 20
Factors of 28 are 1, 2, 4, 7, 28
Hence, the common factors are 1, 2 and 4.

(b) The given numbers are: 15 and 25
Factors of 15 are 1, 3, 5, 15
Factors of 25 are 1, 5, 25
Hence, the common factors are 1 and 5.

(c) The given numbers are: 35 and 50
Factors of 35 are 1, 5, 7, 35
Factors of 50 are 1, 2, 5, 10, 25 50
Hence, the common factors are 1 and 5.

(d) The given numbers are: 56 and 120
Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, 60, 120
Hence, the common factors are 1, 2, 4 and 8.

Ex 3.4 Class 6 Maths Question 2.

Find the common factors of:
(a) 4, 8 and 12
(b) 5, 15 and 25

Solution:
(a) the given numbers are: 4, 8 and 12
Factors of 4 are 1, 2, 4
Factors of 8 are 1, 2, 4, 8
Factors of 12 are 1, 2, 3, 4, 6, 12
Hence, the common factors are 1, 2 and 4.

(b) The given numbers are: 5, 15 and 25
Factors of 5 are 1, 5
Factors of 15 are 1, 3, 5, 15
Factors of 25 are 1, 5, 25
Hence, the common factors are 1 and 5.

Ex 3.4 Class 6 Maths Question 3.

Find first three common multiples of:
(a) 6 and 8
(b) 12 and 18

Solution:
(a) The given numbers are: 6 and 8
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, 80, 88, 96, …
First three common multiples of 6 and 8 are: 24, 48, 72

(b) The given numbers are: 12 and 18
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, 144, 162, 180, …
First three common multiples of 12 and 18 are: 36, 72, 108

Ex 3.4 Class 6 Maths Question 4.

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

Solution:
The given numbers are 3 and 4.
Multiples of 3 less than 100 are:

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

Ex 3.4 Class 6 Maths 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) The given number are: 18 and 35
Factors of 18 are 1, 2, 3, 6, 9, 18
Factors of 35 are 1, 5, 7, 35
Since, the common factors of 18 and 35 is only 1.
Hence, 18 and 35 are co-primes.

(b) The given numbers are: 15 and 37
Factors of 15 are 1, 3, 5, 15
Factors of 37 are 1, 37
Since, the common factor of 15 and 37 is only 1.
Hence, they are co-primes.

(c) The given numbers are: 30 and 415
Factors of 30 are 1, 2, 3, 5, 6, 15, 30
Factors of 415 are 1, 5, 83
Since, the numbers have common factors 1 and 5.
Hence, they are not co-primes.

(d) The given numbers are: 17 and 68
Factors of 17 are 1, 17
Factors of 68 are 1, 2, 4, 17, 34, 68
Since, the numbers have common factors 1 and 17.
Hence, they are not co-primes.

(e) The given numbers are: 216 and 215
Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 54, 72, 108, 216
Factors of 215 are 1, 5, 43
Since, only 1 is the common factor of 216 and 215.
Hence, they are co-primes.

(f) The given numbers are: 81 and 16
Factors of 81 are 1, 3, 9, 27, 81
Factors of 16 are 1, 2, 4, 8, 16
Since, only 1 is the common factor of 81 and 16.
Hence, they are co-primes.

Ex 3.4 Class 6 Maths Question 6.

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

Solution:
Since the number is divisible by both 5 and 12, the number will also be divisible by 5 × 12, i.e., by 60.

Ex 3.4 Class 6 Maths 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, 12.
Since the number is divisible by 12, therefore, the number will also be divisible by its factors, i.e., by 1, 2, 3, 4, 6 and 12.

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