The DAV Class 6 Maths Book Solutions Pdf and **DAV Class 6 Maths Chapter 2 Worksheet 5 **Solutions of Factors and Multiples offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 2 WS 5 Solutions

Question 1.

Find the HCF of the following numbers by the factor method:

(a) 7, 18

Solution:

7, 18

Factors of 7 = , 7

Factors of 18 = 1. 2, 3, 6, 9, 18

Common factor = 1

HCF = 1

(b) 12, 30, 54

Solution:

12, 30, 54

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 30 = 1, , 3, 5, 6, 10, 15, 3

Factors of 54 = 1, 2,3, 6,9, 18, 27, 5

Common factor = 1, 2, 3, 6

∴ Highest common factor (HCF) = 6

(c) 70, 14, 35

Solution:

70, 14, 35

Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70

Factors of 14 = 1, 2, 7, 14

Factors of 35 = 1 5, 7, 35

Common factors = 1 × 7 = 7

∴ HCF = 7

Question 2.

Find the HCF of the following numbers by prime factorisation method:

(a) 76, 28

Solution:

76, 28

76 = 2 × 2 × 19

28 = 2 × 2 × 7

Prime factors of 76 = 2 × 2 × 19

Prime factors of 28 = 2 × 2 × 7

Common factors are 2 and 2.

∴ HCF = 2 × 2 = 4

(b) 24, 16, 36

Solution:

24 = 2 × 2 × 2 × 3 → Prime factors of 24

16 = 2 × 2 × 2 × 2 → Prime factors of 16

36 = 2 × 2 × 3 × 3 → Prime factors of 36

Common factors are 2 and 2.

∴ HCF = 2 × 2 = 4

(c) 38, 64, 82

Solution:

38 = 2 × 19 → Prime factors of 38

64 = 2 × 2 × 2 × 2 × 2 × 2 → Prime factors of 64

32 = 2 × 2 × 2 × 2 × 2 → Prime factors of 32

Common factors is 2.

∴ HCF = 2

Question 3.

Find HCF of the following numbers by continued division method.

(a) 345, 506

Solution:

Here, 506 > 345

Hence, HCF of 345 and 506 is 23

(b) 144, 384, 120

Solution:

Here, 384 > 144 > 120

The HCF of 384 and 144 = 48

Now HCF of 48 and 144 is

Hence, the required HCF = 48

(c) 287, 533

Solution:

Here, 533 > 287

Hence, the required HCF = 41

(d) 208, 494, 949

Solution:

Here, 949 > 494 > 208

Now we have to calculate the HCF of 13 and 208

Hence, HCF of 208, 494, 949 = 13.

(e) 1212, 6868, 1111

Solution:

Here, 6868 > 1212 > 1111

HCF of 6868 and 1212 = 404

Now we have to find the HCF of 1111 and 404

Hence, the required HCF = 101.

(f) 1794, 2346, 4761

Solution:

Here, 4761 > 2346 > 1794

HCF of 2346 and 4761 = 69

Now we have to find the HCF of 69 and 1794

Hence, the required HCF = 69.

(g) 70, 105, 175

Solution:

Here, 175 > 105 > 70

HCF of 175 and 105 = 15

Now we have to find the HCF of 15 and 70.

Hence, the required HCF = 5.

(h) 270, 450, 315

Solution:

Here, 450 > 315 > 270

HCF of 450 and 315 = 45

Now we have to find the HCF of 45 and 270

Hence, the required HCF = 45.

Question 4.

What is the HCF of:

(a) Two consecutive natural numbers

Solution:

1

(b) Two consecutive even numbers

Solution:

2

(c) Two consecutive odd numbers

Solution:

1

(d) Any two prime numbers

Solution:

1

Question 5.

Find the greatest number which divides 203 and 434 leaving remainder 5 in each case.

Solution:

We have to find the numbers which exactly divides

203 – 5 = 198 and

434 – 5 = 429

∴ We have to find the HCF of 198 and 429

Hence, the required number = 33.

Question 6.

Find the greatest number which exactly divides 625 and 1433 leaving remainders 5 and 3 respectively.

Solution:

625 – 5 = 620 and

1433 – 3 = 1430

So we have to find HCF of 620 and 1430

Hence, the required number is 10.

Question 7.

The length, breadth and height of a room are 8.25 m, 6.75 m and 4.50 m respectively. Determine the longest tape which can measure the 3 dimensions of the rooms exactly.

Solution:

8.25 m = 8.25 × 100 cm = 825 cm

6.75 m = 6.75 × 100 cm = 675 cm

4.50 m = 4.50 × 100 cm = 450 cm

Now we have to find the HCF of 825, 675 and 450

HCF of 825 and 675 = 75

Now we have to find the HCF of 75 and 450

Hence, the HCF of the given number = 75

and the measurement of the tape = 75 cm or 0.75 m.

Question 8.

There are 312 mango bites, 260 eclairs and 156 coffee bites in a box. These are to be put in packets so that each packet contains the same number of toffees. Find the maximum number of toffees in each packet.

Solution:

We have to find the HCF of 312, 260 and 156

Now find the HCF of 52 and 156

Hence, the required number of toffees are 52.