## RS Aggarwal Class 6 Solutions Chapter 2 Factors and Multiples Ex 2B

These Solutions are part of RS Aggarwal Solutions Class 6. Here we have given RS Aggarwal Solutions Class 6 Chapter 2 Factors and Multiples Ex 2B.

**Other Exercises**

- RS Aggarwal Solutions Class 6 Chapter 2 Factors and Multiples Ex 2A
- RS Aggarwal Solutions Class 6 Chapter 2 Factors and Multiples Ex 2B
- RS Aggarwal Solutions Class 6 Chapter 2 Factors and Multiples Ex 2C
- RS Aggarwal Solutions Class 6 Chapter 2 Factors and Multiples Ex 2D
- RS Aggarwal Solutions Class 6 Chapter 2 Factors and Multiples Ex 2E
- RS Aggarwal Solutions Class 6 Chapter 2 Factors and Multiples Ex 2F

**Question 1.**

**Solution:**

(i) The given number = 2650

Digit at unit’s place = 0

It is divisible by 2.

(ii) The given number = 69435

Digit at unit’s place = 5

It is not divisible by 2.

(iii) The given number = 59628

Digit at unit’s place = 8

It is divisible by 2.

(iv) The given number = 789403

Digit at unit’s place = 3

It is not divisible by 2.

(v) The given number = 357986

Digit at unit’s place = 6

It is divisible by 2.

(vi) The given number = 367314

Digit at unit’s place = 4

It is divisible by 2.

**Question 2.**

**Solution:**

(i) The given number = 733

Sum of its digits = 7 + 3 + 3 = 13,

which is not divisible by 3.

∴ 733 is not divisible by 3.

(ii) The given number = 10038

Sum of its digits = 1 + 0 + 0 + 3 + 8 = 12,

which is divisible by 3

∴ 10038 is divisible by 3.

(iii) The given number = 20701

Sum of its digits = 2 + 0 + 7 + 0 + 1 = 10,

which is not divisible by 3

∴ 20701 is not divisible by 3.

(iv) The given number = 524781

Sum of its digits = 5 + 2 + 4 + 7 + 8 + 1 = 27,

which is divisible by 3

∴ 524781 is divisible by 3.

(v) The given number = 79124

Sum of its digits = 7 + 9 + 1 + 2 + 4 = 23,

which is not divisible by 3

∴ 79124 is not divisible by 3.

(vi) The given number = 872645

Sum of its digits = 8 + 7 + 2 + 6 + 4 + 5 = 32,

which is not divisible by 3

∴ 872645 is not divisible by 3.

**Question 3.**

**Solution:**

(i) The given number = 618

The number formed by ten’s and unit’s digits is 18, which is not divisible by 4.

∴ 618 is not divisible by 4.

(ii) The given number = 2314

The number formed by ten’s and unit’s digits is 14, which is not divisible by 4.

∴ 2314 is not divisible by 4.

(iii) The given number = 63712

The number formed by ten’s and unit’s digits is 12, which is divisible by 4

∴ 63712 is divisible by 4.

(iv) The given number = 35056

The number formed by ten’s and unit’s digits is 56, which is divisible by 4.

∴ 35056 is divisible by 4.

(v) The given number = 946126

The number formed by ten’s and unit’s digits is 26, which is not divisible by 4.

∴ 946126 is not divisible by 4.

(vi) The given number = 810524

The number formed by ten’s and unit’s digits is 24, which is divisible by 4.

∴ 810524 is divisible by 4.

**Question 4.**

**Solution:**

We know that a number is divisible by 5 if its ones digit is 0 or 5

(i) 4965, (ii) 23590 (iv) 723405 and (vi) 438750 are divisible by 5

**Question 5.**

**Solution:**

(i) The given number = 2070

Its unit’s digit = 0

So, it is divisible by 2

Sum of its digits = 2 + 0 + 7 + 0 = 9,

which is divisible by 3

∴ The given number is divisible by 3.

So, 2070 is divisible by both 2 and 3.

Hence it is divisible by 6.

(ii) The given number = 46523

Its unit’s digit = 3

So, it is not divisible by 2

Hence 46523 is not divisible by 6.

(iii) The given number = 71232

Its unit’s digit = 2

So, it is divisible by 2

Sum of its digits = 7 + 1 + 2 + 3 + 2

= 15, which is divisible by 3

∴ 71232 is divisible by both 2 and 3

Hence it is divisible by 6.

(iv) The given number = 934706

Its unit’s digit = 6 So,

it is divisible by 2

Sum of its digits = 9 + 3 + 4 + 7 + 0 + 6 = 29,

which is not divisible by 3

Hence 934706 is not divisible by 6.

(v) The given number = 251780

Its unit’s digit = 0

So, it is divisible by 2

Sum of its digits = 2 + 5 + 1 + 7 + 8 + 0 = 23,

which is not divisible by 3

251780 is not divisible 6

(vi) 872536 is not divisible by 6 as sum of its digits is 8 + 7 + 2 + 5 + 3 + 6 = 31 which is not divisible by 3

**Question 6.**

**Solution:**

We know that a number is divisible by 7 if the difference between twice the ones digit and the number formed by the other digits is either 0 or a multiple of 7

(i) 826, 6 x 2 = 12 and 82

Difference between 82 and 12 = 70

Which is divisible by 7

∴ 826 is divisible by 7

(ii) In 117, 7 x 2 = 14, 11

Difference between 14 and 11 = 14 – 11 = 3

Which is not divisible by 7

∴ 117 is not divisible by 7

(iii) In 2345, 5 x 2 = 10 and 234

Difference between 234 – 10 = 224

which is divisible by 7

∴ 2345 is divisible by 7

(iv) In 6021, 1 x 2 = 2, and 602

Difference between 602 and 2 = 600

which is not divisible by 7

∴ 6021 is not divisible by 7

(v) In 14126, 6 x 2 = 12 and 1412

Difference between 1412 – 12 = 1400

which 8 is divisible by 7

∴ 14126 is divisible by 7

(vi) In 25368, 8 x 2 = 16 and 2536

Difference between 2536 and 16 = 2520

which is divisible by 7

∴ 25368 is divisible by 7

**Question 7.**

**Solution:**

(i) The given number = 9364

The number formed by hundred’s, ten’s and unit’s digits is 364, which is not divisible by 8.

∴ 9364 is not divisible by 8.

(ii) The given number = 2138

The number formed by hundred’s, ten’s and unit’s digits is 138, which is not divisible by 8.

∴ 2138 is not divisible by 8.

(iii) The given number = 36792

The number formed by hundred’s, ten’s and unit’s digits is 792, which is divisible by 8.

∴ 36792 is divisible by 8.

(iv) The given number = 901674

The number formed by hundred’s, ten’s and unit’s digits is 674, which is not divisible by 8.

∴ 901674 is not divisible by 8.

(v) The given number = 136976

The number formed by hundred’s, ten’s and unit’s digits is 976, which is divisible by 8.

∴ 136976 is divisible by 8.

(vi) The given number = 1790184

The number formed by hundred’s, ten’s and unit’s digits is 184, which is divisible by 8.

∴ 1790184 is divisible by 8.

**Question 8.**

**Solution:**

We know that a number is divisible by 9, if the sum of its digits is divisible by 9

(i) In 2358

Sum of digits : 2 + 3 + 5 + 8 = 18

which is divisible by 9

∴ 2358 is divisible by 9

(ii) In 3333

Sum of digits 3 + 3 + 3 + 3 = 12

which is not divisible by 9

∴ 3333 is not divisible by 9

(iii) In 98712

Sum of digits = 9 + 8 + 7 + 1 + 2 = 27

Which is divisible by 9

∴ 98712 is divisible by 9

(iv) In 257106

Sum of digits = 2 + 5 + 7 + 1 + 0 + 6 = 21

which is not divisible by 9

∴ 257106 is not divisible by 9

(v) In 647514

Sum of digits = 6 + 4 + 7 + 5 + 1 + 4 = 27

which is divisible by 9

∴ 647514 is divisible by 9

(v) In 326999

Sum of digits = 3 + 2 + 6 + 9 + 9 + 9 = 38

which is not divisible by 9

∴ 326999 is divisible by 9

**Question 9.**

**Solution:**

We know that a number is divisible by 10 if its ones digit is 0

∴(i) 5790 is divisible by 10

**Question 10.**

**Solution:**

(i) The given number = 4334

Sum of its digits in odd places = 4 + 3 =7

Sum of its digits in even places = 3 + 4 = 7

Difference of the two sums = 7 – 7 = 0

∴4334 is divisible by 11.

(ii) The given number = 83721

Sum of its digits in odd places = 1 + 7 + 8 = 16

Sum of its digits in even places = 2 + 3 = 5

Difference of the two sums = 16 – 5 = 11,

which is multiple of 11.

∴ 83721 is divisible by 11.

(iii) The given number = 66311

Sum of its digits in odd places = 1 + 3 + 6 = 10

Sum of its digits in even places = 1 + 6 = 7

Difference of the two sums = 10 – 7 = 3,

which is not a multiple of 11.

∴ 66311 is not divisible by 11.

(iv) The given number = 137269

Sum of its digits in odd places = 9 + 2 + 3 = 14

Sum of its digits in even places = 6 + 7 + 1 = 14

Difference of the two sums = 14 – 14 = 0

∴ 137269 is divisible by 11.

(v) The given number = 901351

Sum of its digits in odd places = 1 + 3 + 0 = 4

Sum of its digits in even places = 5 + 1 + 9 = 15

Difference of the two sums = 15 – 4 = 11,

which is a multiple of 11.

∴ 901351 is divisible by 11.

(vi) The given number = 8790322

Sum of its digits in odd places = 2 + 3 + 9 + 8 = 22

Sum of its digits in even places = 2 + 0 + 7 = 9

Difference of the two sums = 22 – 9 = 13,

which is not a multiple of 11.

∴ 8790322 is not divisible by 11.

**Question 11.**

**Solution:**

(i) The given number = 27*4

Sum of its digits = 2 + 7 + 4 = 13

The number next to 13 which is divisible by 3 is 15.

∴ Required smallest number = 15 – 13

= 2.

(ii) The given number = 53*46

Sum of the given digits = 5 + 3 + 4 + 6 = 18,

which is divisible by 3.

∴ Required smallest number = 0.

(iii) The given number = 8*711

Sum of the given digits = 8 + 7 + 1 + 1 = 17

The number next to 17,

which is divisible by 3 is 18.

∴ Required smallest number =18 – 17 = 1

(iv) The given number = 62*35

Sum of the given digits = 6 + 2 + 3 + 5 = 16

The number next to 16,

which is divisible by 3 is 18.

∴ Required smallest number =18 – 16 = 2

(v) The given number = 234*17

Sum of the given digits = 2 + 3+ 4 + 1 + 7 = 17

The number next to 17, which is divisible by 3 is 18.

Required smallest number = 18 – 17 = 1.

(vi) The given number = 6* 1054

Sum of the given digits = 6 + 1+ 0 + 5 + 4 = 16

The number next to 16,

which is divisible by 3 is 18.

Required smallest number = 18 – 16 = 2.

**Question 12.**

**Solution:**

(i) The given number = 65*5

Sum of its given digits = 6 + 5 + 5 = 16

The number next to 16, which is divisible by 9 is 18.

∴ Required smallest number =18 – 16 = 2

(ii) The given number = 2*135

Sum of its given digits = 2 + 1 + 3 + 5

The number next to 11, which is divisible by 9 is 18.

∴ Required smallest number = 18 – 11 =7.

(iii) The given number = 6702*

Sum of its given digits = 6 + 7 + 0 + 2 = 15

The number next to 15, which is divisible by 9 is 18.

∴ Required smallest number = 18 – 15 = 3

(iv) The given number = 91*67

Sum of its given digits = 9 + 1 + 6 + 7 =23

The number next to 23, which is divisible by 9 is 27.

∴ Required smallest number = 27 – 23 = 4.

(v) The given number = 6678*1

Sum of its given digits= 6 + 6 + 7 + 8 + 1 = 28

The number next to 28, which is divisible by 9 is 36.

∴ Required smallest number = 36 – 28 = 8.

(vi) The given number = 835*86

Sum of its given digits = 8 + 3 + 5 + 8 + 6 = 30

The number next to 30, which is divisible by 9 is 36.

∴ Required smallest number = 36 – 30 = 6.

**Question 13.**

**Solution:**

(i) The given number = 26*5

Sum of its digits is odd places = 5 + 6 = 11

Sum of its digits in even places = * + 2

Difference of the two sums = 11 – (* + 2)

The given number will be divisible by 11 if the difference of the two sums = 0.

∴ 11 – (* + 2) = 0

11 = * + 2

11 – 2 = *

9 = *

Required smallest number = 9.

(ii) The given number = 39*43

Sum of its digits in odd places

=3 + * + 3 = * + 6

Sum of its digits in even places = 4 + 9 = 13

Difference of the two sums = * + 6 – 13 = * – 7

The given number will be divisible by 11, if the difference of the two sums = 0.

∴ * – 7 = 0

* = 7

∴ Required smallest number = 7.

(iii) The given number = 86*72

Sum of its digits in odd places

= 2 + * + 8 = * + 10

Sum of its digits in even places = 7 + 6 = 13

Difference of the two sums = * + 10 – 13 = * – 3

The given number will be divisible by 11, if the difference of the two sums = 0.

∴ * – 3 = 0

* = 3

∴ Required smallest number = 3.

(iv) The given number = 467*91

Sum of its digits in odd places = 1 + * + 6 = * + 7

Sum of its digits in even places = 9 + 7 + 4 = 20

Difference of the two sums

= 20 – (* + 7)

= 20 – * – 7 = 13 – *

Clearly the difference of the two sums will be multiple of 11 if 13 – * = 11

∴ 13 – 11 = *

2 = *

* = 2 .

∴ Required smallest number = 2.

(v) The given number = 1723*4

Sum of its digits in odd places = 4 + 3 + 7 = 14

Sum of its digits in even places = * + 2 + 1 = * + 3

Difference cf the two sums = * + 3 – 14 = * – 11

The given number will be divisible by 11,if *- 11 is a multiple of 11,which is possible if * = 0.

Required smallest number = 0.

(vi) The given number = 9*8071

Sum of its digits in odd places = 1 + 0 + * = 1 + *

Sum of its digits in even places = 7 + 8 + 9 = 24

Difference of the two sums = 24 – 1 – * = 23 – *

∴ The given number will be divisible by 11, if 23 – * is a multiple of 11, which is possible if * = 1.

∴ Required smallest number = 1.

**Question 14.**

**Solution:**

(i) The given number = 10000001

Sum of its digits in odd places

= 1 + 0 + 0 + 0 = 1

Sum of its digits in even places = 0 + 0 + 0 + 1 = 1

Difference of the two sums = 1 – 1 = 0

∴ The number 10000001 is divisible by 11.

(ii) The given number = 19083625

Sum of its digits in odd places

= 5 + 6 + 8 + 9 = 28

Sum of its digits in even places = 2 + 3 +0 + 1 = 6

Difference of the two sums = 28 – 6 = 22,

which is divisible by 11.

∴ The number 19083625 is divisible by 11.

(iii) The given number = 2134563

Sum of its digits

= 2 + 1 + 3 + 4 + 5 + 6 + 3 = 24,

which is not divisible by 9.

∴ The number 2134563 is not divisible by 9.

(iv) The given number = 10001001

Sum of its digits

= 1 + 0 + 0 + 0 + 1 + 0 + 0 + 1 = 3,

which is divisible by 3.

∴ The number 10001001 is divisible by 3.

(v) The given number = 10203574

The number formed by its ten Is and unit’s digits is 74, which is not divisible by 4.

The number 10203574 is not divisible by 4.

(vi) The given number = 12030624

The number formed by its hundred’s, ten’s and unit’s digits = 624,

which is divisible by 8.

∴ The number 12030624 is divisible by

**Question 15.**

**Solution:**

103, 137, 179, 277, 331, 397 are prime numbers.

**Question 16.**

**Solution:**

(i) 154

(ii) 612

(iii) 5112, 3816 etc.

(iv) 3426, 5142 etc.

**Question 17.**

**Solution:**

(i) False

(ii) True

(iii) False

(iv) True

(v) False

(vi) True

(vii) True

(viii) True

Hope given RS Aggarwal Solutions Class 6 Chapter 2 Factors and Multiples Ex 2B are helpful to complete your math homework.

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