The DAV Class 6 Maths Book Solutions Pdf and **DAV Class 6 Maths Chapter 2 Worksheet 1 **Solutions of Factors and Multiples offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 2 WS 1 Solutions

Question 1.

Fill in the following blanks:

(a) Numbers which have more than 2 factors are called _________

Solution:

Composite numbers

(b) Numbers which are not divisible by any other number except 1 and the number itself are called _________.

Solution:

Prime numbers

(c) 1 is neither _________ nor composite.

Solution:

Prime

(d) 6 is a composite number as it has _________ factors.

Solution:

4

(e) _________ is the only even prime number.

Solution:

2

(f) The smallest prime number is _________

Solution:

2

(g) The smallest composite number is _________

Solution:

4

(h) The smallest odd composite number is _________.

Solution:

9

(i) The greatest 2-digit prime number is _________.

Solution:

97

Question 2.

Are the following numbers prime or composite. Show by finding factors.

(a) 9

Solution:

We have

1 × 9 = 9

3 × 3 = 9

Factors of 9 are 1, 3, 9.

Therefore 9 is a composite number.

(b) 48

Solution:

We have

1 × 48 = 48

2 × 24 = 48

3 × 16 = 48

4 × 12 = 48

6 × 8 = 48

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 49.

Therefore 48 is a composite number.

(c) 89

Solution:

We have

1 × 89 = 89

Factors of 89 are 1 and 89.

Therefore, 89 is a prime number.

(d) 96

Solution:

We have

1 × 96 = 96

2 × 48 = 96

3 × 32 = 96

4 × 24 = 96

6 × 16 = 96

8 × 12 = 96

Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 24, 32, 48, 96

Therefore, 96 is a composite number.

(e) 78

Solution:

We have

1 × 78 = 78

2 × 39 = 78

3 × 26 = 78

6 × 13 = 78

Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78.

Therefore, 78 is a composite number.

(f) 101

Solution:

We have

1 × 101 = 101

Factors of 101 are 1 and 101.

Therefore, 101 is a prime number.

Question 3.

Write down the first ten prime numbers.

Solution:

First ten prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Question 4.

Write down all the prime numbers between 50 and 110.

Solution:

Prime numbers between 50 and 110 are:

53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109.

Question 5.

A number lies between 2000 and 2070 and has 5 in its ones place. Is it a prime or composite number? Give reasons.

Solution:

It is a composite number and it may have more than two factors. The number between 2000 and 2070 can be divisible by 3, 5 and 5 and 25.

Question 6.

List the first five multiples of:

(a) 25

Solution:

25 = 25 × 1 = 25,

25 × 2 = 50,

25 × 3 = 75,

25 × 4 = 100,

25 × 5 = 125

Hence, the first 5 multiples of 25 are 25, 50, 75, 100, 125.

(b) 17

Solution:

17 = 17 × 1 = 17,

17 × 2 = 34,

17 × 3 = 51,

17 × 4 = 68,

17 × 5 = 85

Hence, the first 5 multiples of 17 are 17, 34, 51, 68, 85.

(c) 100

Solution:

100 = 100 × 1 = 100,

100 × 2 = 200,

100 × 3 = 300,

100 × 4 = 400,

100 × 5 = 500

Hence, the first 5 multiples of 100 are 100, 200, 300, 400, 500.

(d) 41

Solution:

41 × 1 = 41,

41 × 2 = 82,

41 × 3 = 123,

41 × 4 = 164,

41 × 5 = 205

Question 7.

List all multiples of 15 between 50 and 100.

Solution:

Multiples of 15 between 50 and 100 are

15 × 3 = 45,

15 × 4 = 60,

15 × 5 = 75,

15 × 6 = 90

Hence, the required multiples are 45, 60, 75 and 90.

Question 8.

Between which multiples of 10 does 3486 lie?

Solution:

The multiple of 10 below 3486 is 3480 and the multiple of 10 above 3480 is 3490.

Hence, the required numbers are 3480 and 3490.

Question 9.

Write any four pairs of twin primes.

Solution:

(3, 5), (5, 7), (11, 13), (17, 19).

Question 10.

Which of the following numbers are co-prime?

(a) 13, 14

Solution:

13, 14

13 and 14 have no common factor

∴ They are co-prime numbers.

(b) 8, 20

Solution:

8, 20

8 and 20 have 2 and 4 common factors

∴ They are not co-prime numbers.

(c) 31, 59

Solution:

31, 59

31 and 59 have no common factors

∴ They are co-prime numbers.

(d) 34, 85

Solution:

34, 85

34 and 85 have 17 as common factor

∴ They are not co-prime numbers.

### DAV Class 6 Maths Chapter 2 Worksheet 1 Notes

Prime numbers:

The numbers which are divisible by only 1 and itself are called the Prime Numbers. 2 is the smallest prime number.

Example: 2, 3, 5, 7, 11, 13, 17, 19 ………..

Twin prime numbers:

The two prime numbers whose difference is 2 are called twin prime numbers.

Example: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31) …………

Coprime numbers:

Any two numbers which have no common factor are called co-prime numbers.

Example: 2 and 3, 3 and 5, 6 and 7, 9 and 10 etc.

Composite numbers:

A number which has more than two factors are called composite numbers.

Example: 4, 6, 8, 12, 16 ……….

Multiples:

Multiplication table of a number gives its multiples.

Example: Multiples of 2 are 2, 4, 6, 8, 10, 12 ……….

Factors:

Any non-zero number which divides a number completely leaving no remainder is called its factor.

Example:

Factors of 6 are 1, 2, 3, 6 …………..

Note:

(i) 1 is a factor of every number

(ii) Every number is a factor of itself.

Example 1:

Select the prime and composite numbers from the given numbers:

(a) 12

Solution:

12 = 1 × 12,

12 = 2 × 6,

12 = 3 × 4

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

Therefore, 12 is a composite number.

(b) 17

Solution:

17 = 1 × 17

17 has two factors 1 and 17

17 is a prime number.

(c) 36

Solution:

36 = 1 × 36,

36 = 2 × 18,

36 = 3 × 12,

36 = 4 × 9,

36 = 6 × 6

Factors of 36 are 1, 2, 3, 4, 6, 12, 18 and 36

Hence, 36 is a composite number.

(d) 20

Solution:

20 = 1 × 20,

20 = 2 × 10,

20 = 4 × 5

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

So, 20 is a composite number.

Example 2:

Find the 3 multiples of each of the following:

(a) 5

Solution:

Multiples of 5 are

5 × 1 = 5,

5 × 2 = 10,

5 × 3 = 15

(b) 7

Solution:

Multiples of 7 are

7 × 1 = 7,

7 × 2 = 14,

7 × 3 = 21

(c) 12

Solution:

Multiples of 12 are

12 × 1 = 12,

12 × 2 = 24,

12 × 3 = 36

(d) 20

Solution:

Multiples of 20 are

20 × 1 = 20,

20 × 2 = 40,

20 × 3 = 60