The document RD Sharma Solutions: Exercise 2.1- Playing With Numbers Class 6 Notes | EduRev is a part of the Class 6 Course Mathematics (Maths) Class 6.

All you need of Class 6 at this link: Class 6

**Q.1. ****Define**

**(i) factor**

**(ii) multiple**

**Give four examples of each.**

**Ans: **

**(i) **Factor: A factor of a number is an exact divisor of that number.

For example, 4 exactly divides 32. Therefore, 4 is a factor of 32.

Examples of factors are:

2 and 3 are factors of 6 because 2 × 3 = 6

2 and 4 are factors of 8 because 2 × 4 = 8

3 and 4 are factors of 12 because 3 × 4 = 12

3 and 5 are factors of 15 because 3 × 5 = 15

**(ii)** Multiple: When a number 'a' is multiplied by another number 'b', the product is the multiple of both the numbers 'a' and 'b'.

Examples of multiples:

6 is a multiple of 2 because 2 × 3 = 6

8 is a multiple of 4 because 4 × 2 = 8

12 is a multiple of 6 because 6 × 2 = 12

21 is a multiple of 7 because 7 × 3 = 21

**Q.2. ****Write all factors of each of the following numbers:**

**(i) 60**

**(ii) 76**

**(iii) 125**

**(iv) 729**

**Ans: **

**(i)** 60 = 1 × 60

60 = 2 × 30

60 = 3 × 20

60 = 4 × 15

60 = 5 × 12

60 = 6 × 10

∴ The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

**(ii) **76 = 1 × 76

76 = 2 × 38

76 = 4 × 19

∴ The factors of 76 are 1, 2, 4, 19, 38 and 76.

**(iii) **125 = 1 × 125

125 = 5 × 25

∴ The factors of 125 are 1, 5, 25 and 125.

**(iv) **729 = 1 × 729

729 = 3 × 243

729 = 9 × 81

729 = 27 × 27

∴ The factors of 729 are 1, 3, 9, 27, 81, 243 and 729.

**Q.3. ****Write first five multiples of each of the following numbers:**

**(i) 25**

**(ii) 35**

**(iii) 45**

**(iv) 40**

**Ans: **

**(i)** The first five multiples of 25 are as follows:

25 × 1 = 25

25 × 2 = 50

25 × 3 = 75

25 × 4 = 100

25 × 5 = 125

**(ii)** The first five multiples of 35 are as follows:

35 × 1 = 35

35 × 2 = 70

35 × 3 = 105

35 × 4 = 140

35 × 5 = 175

**(iii) **The first five multiples of 45 are as follows:

45 × 1 = 45

45 × 2 = 90

45 × 3 = 135

45 × 4 = 180

45 × 5 = 225

**(iv)** The first five multiples of 40 are as follows:

40 × 1 = 40

40 × 2 = 80

40 × 3 = 120

40 × 4 = 160

40 × 5 = 200

**Q.4. ****Which of the following numbers have 15 as their factor?**

**(i) 15615**

**(ii) 123015**

**Ans: **

**(i) **15 is a factor of 15,615 because it is a divisor of 15,615.

i.e., 1041 × 15 = 15,615

**(ii) **15 is a factor of 1,23,015 because it is a divisor of 1,23,015.

i.e., 8,201 × 15 = 1,23,015

Thus, both the given numbers have 15 as their factor.

Disclaimer: The answer given in the book is incorrect.

**Q.5. ****Which of the following numbers are divisible by 21?**

**(i) 21063**

**(ii) 20163**

**Ans: **We know that a given number is divisible by 21 if it is divisible by each of its factors.

The factors of 21 are 1, 3, 7 and 21.

**(i) **Sum of the digits of the given number = 2 + 1 + 0 + 6 + 3 = 12 which is divisible by 3.

Hence, 21,063 is divisible by 3.

Again, a number is divisible by 7 if the difference between twice the one's digit and the number formed by the other digits is either 0 or a multiple of 7.

2,106 − (2 × 3) = 2,100 which is a multiple of 7.

Thus, 21,063 is divisible by 21.

**(ii)** Sum of the digits of the given number = 2 + 0 + 1 + 6 + 3 = 12 which is divisible by 3.

Hence, 20,163 is divisible by 3.

Again, a number is divisible by 7 if the difference between twice the one's digit and the number formed by the other digits is either 0 or multiple of 7.

2016 − (2 × 3) = 2010 which is not a multiple of 7.

Thus, 20,163 is not divisible by 21.

**Q.6. ****Without actual division show that 11 is a factor of each of the following numbers:**

**(i) 1111**

**(ii) 11011**

**(iii) 110011**

**(iv) 1100011**

**Ans: **

**(i) **1,111

The sum of the digits at the odd places = 1 + 1 = 2

The sum of the digits at the even places = 1 + 1 = 2

The difference of the two sums = 2 − 2 = 0

∴ 1,111 is divisible by 11 because the difference of the sums is zero.

**(ii) **11,011

The sum of the digits at the odd places = 1 + 0 + 1 = 2

The sum of the digits at the even places = 1 + 1 = 2

The difference of the two sums = 2 − 2 = 0

∴ 11,011 is divisible by 11 because the difference of the sums is zero.

**(iii)** 1,10,011

The sum of the digits at the odd places = 1 + 0 + 1 = 2

The sum of the digits at the even places = 1 + 0 + 1 = 2

The difference of the two sums = 2 − 2 = 0

∴ 1,10,011 is divisible by 11 because the difference of the sums is zero.

**(iv) **11,00,011

The sum of the digits at the odd places = 1 + 0 + 0 + 1 = 2

The sum of the digits at the even places = 1 + 0 + 1 = 2

The difference of the two sums = 2 − 2 = 0

∴ 11,00,011 is divisible by 11 because the difference of the sums is zero.

**Q.7. ****Without actual division show that each of the following numbers is divisible by 5:**

**(i) 55**

**(ii) 555**

**(iii) 5555**

**(iv) 50005**

**Ans: **A number will be divisible by 5 if the unit's digit of that number is either 0 or 5.

**(i) **In 55, the unit's digit is 5. Hence, it is divisible by 5.

**(ii) **In 555, the unit's digit is 5. Hence, it is divisible by 5.

**(iii) **In 5,555, the unit's digit is 5. Hence, it is divisible by 5.

**(iv)** In 50,005, the unit's digit is 5. Hence, it is divisible by 5.

**Q.8. Is there any natural number having no factor at all?**

**Ans: **No, because each natural number is a factor of itself.

**Q.9. Find numbers between 1 and 100 having exactly three factors.**

**Ans: **The numbers between 1 and 100 having exactly three factors are 4, 9, 25, and 49.

The factors of 4 are 1, 2 and 4.

The factors of 9 are 1, 3 and 9.

The factors of 25 are 1, 5 and 25.

The factors of 49 are 1, 7 and 49.

**Q.10. ****Sort out even and odd numbers:**

**(i) 42**

**(ii) 89**

**(iii) 144**

**(iv) 321**

**Ans: **

A number which is exactly divisible by 2 is called an even number.

Therefore, 42 and 144 are even numbers.

A number which is not exactly divisible by 2 is called an odd number.

Therefore, 89 and 321 are odd numbers.

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

191 videos|221 docs|43 tests

- RD Sharma Solutions: Exercise 2.2- Playing With Numbers
- RD Sharma Solutions: Exercise 2.3- Playing With Numbers
- RD Sharma Solutions: Exercise 2.4- Playing With Numbers
- RD Sharma Solutions: Exercise 2.5- Playing With Numbers
- RD Sharma Solutions: Exercise 2.6- Playing With Numbers
- RD Sharma Solutions: Exercise 2.6- Playing With Numbers