The DAV Class 6 Maths Book Solutions Pdf and **DAV Class 6 Maths Chapter 2 Worksheet 3 **Solutions of Factors and Multiples offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 2 WS 3 Solutions

Question 1.

Look at the following group of numbers and fill in the blanks:

(a) 389510, 7781450, 4203324, 12342

The numbers divisible by 3 are _______ and _______.

Solution:

4203324, 12342

(b) 3437712, 4222910, 6880172, 9811602

The numbers divisible by 9 are _______ and _______.

Solution:

3437712, 9811602

(c) 362442, 8502153, 774067, 46627207

The numbers divisible by 11 are _______ and _______.

Solution:

8502153, 46627207

Question 2.

Pick out the numbers from the following that are divisible by 3 but not by 9.

(a) 38721

Solution:

38721 is divisible by 3 but not divisible by 9

(b) 422679

Solution:

422679 is divisible by 3 but not divisible by 9

(c) 6110586

Solution:

6110586 is divisible by 3 and 9 both.

(d) 257796

Solution:

257796 is divisible by 3 and 9 both.

Question 3.

Test the following for the divisibility by 3 and 9.

(a) 294414

Solution:

294414

Sum of the digits of the number 294414 is

2 + 9 + 4 + 4 + 1 + 4 = 24 + 3 = 8

Hence, 294414 is divisible by 3.

(b) 145404

Solution:

145404

Sum of the digits of the number 145404 is

1+4 + 5 + 4 + 0 + 4=18 + 9 = 2

Hence, 145404 is divisible by 9.

(c) 99999

Solution:

99999

The sum of digits of the number 99999 is

9 + 9 + 9 + 9 + 9 = 45 + 9 = 5

Hence, 99999 is divisible by 9.

Question 4.

Test the divisibility of the following numbers by 11:

(a) 86611291

Solution:

86611291

Sum of the digits at odd places is 8 + 6 + 1 + 9 = 24

Sum of the digits at even places is 6 + 1 + 2 + 1 = 10

Difference 24 – 10 = 14 is not divisible by 11

Hence, 86611291 is not divisible by 11.

(b) 100001

Solution:

100001

Sum of the digits at odd places is 1 + 0 + 0 = 1

Sum of the digits at even places is 0 + 0 + 1 = 1

Difference 1 – 1 = 0

Hence, 100001 is divisible by 11.

(c) 9427355

Solution:

9427355

Sum of the digits at odd places is 9 + 2 + 3 + 5 = 19

Sum of the digits at even places is 4 + 7 + 5 = 16

Difference 19 – 16 = 3 is not divisible by 11

Hence, 9427355 is not divisible by 11.

(d) 7023643

Solution:

7023643

The sum of the digits at odd places is 9 + 2 + 3 + 5 = 19

Sum of the digits at even places is 4 + 7 + 5 = 16

Difference 19 – 16 = 3 is not divisible by 11

Hence, 7023643 is not divisible by 11.

(e) 58334661

Solution:

58334661

Sum of the digits at odd places is 5 + 3 + 4 + 6 = 18

Sum of the digits at even places is 8 + 3 + 6 + 1 = 18

Difference 18 – 18 = 0

Hence, 58334661 is divisible by 11.

(f) 602111213

Solution:

602111213

Sum of the digits at odd places is 6 + 2+1 + 2 + 3 = 14

Sum of the digits at even places is 0 + 1 + 1 + 1 = 3

Difference 14 – 3 = 11 divisible by 11

Hence, 602111213 is divisible by 11.

Question 5.

Fill in the blanks:

(a) A number is divisible by 6 if it is divisible by its two co-prime factors _______ and _______.

Solution:

2, 3

(b) 43185 is divisible by 15 as it is divisible by _______ and _______.

Solution:

3, 5

(c) The number 8625 is not divisible by 6 as it is divisible by _______ but not by _______.

Solution:

3, 2

(d) The number 54420 is divisible by 12 as it is divisible by _______ and _______.

Solution:

4, 3

(e) The number 781022 is divisible by 11 as the difference of the sum of the digits at odd places and the sum of the digits at even places is _______.

Solution:

0

Question 6.

Replace ___ by a digit so that the number is divisible by 9.

(a) 384 ___ 62

Solution:

4

(b) 1 ___ 80498

Solution:

6

(c) 9080 ___

Solution:

1

(d) 46 ___ 21

Solution:

5

Question 7.

Write ‘True’ or ‘False’ for the following statements:

(a) If a number is divisible by 3, it must be divisible by 9.

Solution:

False

(b) If a number is divisible by 18, it must be divisible by 6 and 3.

Solution:

True

(c) If a number is divisible by both 9 and 10, then it must be divisible by 90.

Solution:

True

(d) All numbers which are divisible by 8 are divisible by 4.

Solution:

True

(e) If a number is exactly divisible by two numbers separately then it must be exactly divisible by their sum.

Solution:

False