## RS Aggarwal Class 6 Math Second Chapter Factors And Multiples Exercise 2B Solution

## EXERCISE 2B

**1. Test the divisibility of the following numbers by 2:**

(i) 2650

= Yes, because the last digit is 0.

(ii) 69435

= No, Because the last digit is an odd number.

(iii) 59628

=Yes, Because the last digit is 8.

(iv) 789403

= No, Because the last digit is an odd number.

(v) 357986

= Yes, Because the last digit is 6.

(vi) 367314

= Yes, Because the last digit is 4.

**2. Test the divisibility of the following numbers by 3:**

(i) 733

=7+ 3+ 3

=13

Then, 13 is not divisible by 3. So, its not.

(ii) 10038

= 1+0 +0+ 3+ 8

=12

Then, 12 is divisible by 3.

(iii) 20701

= 2+ 0+ 7+ 0+ 1

= 10

Then, 10 is not divisible by 3. So, its not.

(iv) 524781

= 5+ 2+ 4+ 7+ 8+ 1

= 27

Then, 27 is divisible by 3.

(v) 79124

= 7+ 9+ 1+ 2+ 4

=23

Then, 23 is not divisible by 3. So, its not.

(vi) 872645

= 8+ 7+ 2+ 6+ 4+ 5

= 32

Then, 32 is not divisible by 3. So, its not.

**3. Test the divisibility of the following numbers by 4:**

(i) 618

= The number formed by the tens and ones digits is 18, which is not divisible by 4.

Therefore, 618 is not divisible by 4.

(ii) 2314

= The number formed by the tens and ones digits is 14, which is not divisible by 4.

Therefore, 2314 is not divisible by 4.

(iii) 63712

= The number formed by the tens and ones digits is 12, which is divisible by 4.

Therefore, 63712 is divisible by 4.

(iv) 35056

= The number formed by the tens and ones digits is 56, which is divisible by 4.

Therefore, 35056 is divisible by 4.

(v) 946126

= The number formed by the tens and ones digits is 26, which is not divisible by 4.

Therefore, 946126 is not divisible by 4.

(vi) 810524

= The number formed by the tens and ones digits is 24, which is divisible by 4.

Therefore, 810524 is divisible by 4.

**4. Test the divisibility of the following numbers by 5:**

(i) 4965

= Here the last digit is 5. Therefore, 4965 is divisible by 5.

(ii) 23590

= Here the last digit is 0. Therefore, 23590 is divisible by 5.

(iii) 35208

= Here the last digit is 8. Therefore, 35208 is not divisible by 5.

(iv) 723405

= Here the last digit is 5. Therefore, 723405 is divisible by 5.

(v) 124684

= Here the last digit is 4. Therefore, 124684 is not divisible by 5.

(vi) 438750

= Here the last digit is 0. Therefore, 438750 is divisible by 5.

**5. Test the divisibility of the following numbers by 6:**

(i) 2070

**Ans:** *Here the number divisible by 2, because the last digit of this number is 0.*

*And, sum of digits*

* 2+ 0+7+ 0*

*= 9, which is divisible by 3.*

* Therefore, 2070 is divisible by 6.*

(ii) 46523

**Ans:** Here the number not divisible by 2, because the last digit of this number is an odd number.

*And, sum of digits*

*4+ 6+ 5+ 2+ 3*

*=20, which is not divisible by 3.*

*Therefore, 46523 is not divisible by 6.*

(iii) 71232

**Ans:** Here the number divisible by 2, because the last digit of this number is 2.

*And, sum of digits*

*7+ 1+ 2+ 3+ 2*

*= 15. Which is divisible by 3.*

*Therefore, 71232 is divisible by 6.*

(iv) 7934706

*Ans:* *Here the number divisible by 2, because the last digit of this number is 6.*

*And, sum of digits *

*7+ 9+ 3+ 4+ 7+ 0+ 6*

*= 36, Which is divisible by 3.*

*Therefore, 7934706 is divisible by 6.*

(v) 251780

*Ans:**Here the number divisible by 2, because the last digit of this number is 0.*

*And, sum of digits*

*2+ 5+ 1+ 7+ 8+ 0*

*= 23. Which is not divisible by 3.*

*Therefore, 251780 is not divisible by 6.*

(vi) 872536

**Ans:** Here the number divisible by 2, because the last digit of this number is 6.

*And, sum of digits*

*8+ 7+ 2+ 5+ 3+ 6*

*= 31. Which is not divisible by 3.*

*Therefore, 872536 is not divisible by 6.*

**6. Test the divisibility of the following numbers by 7:**

(i) 826

**Ans:** Clearly, (82 – 2 x 6)= 70. Which is divisible by 7.

*Therefore, 826 is divisible by 7.*

(ii) 117

**Ans:** Clearly, (2 x 7) – 11= 3. Which is not divisible by 7.

*Therefore, 117 is not divisible by 7.*

(iii) 2345

**Ans:** Clearly, (234-2 x 5)= 224. Which is divisible by 7.

*Therefore, 2345 is divisible by 7.*

(iv) 6021

**Ans:** Clearly, (602-2 x 1)= 600. Which is not divisible by 7.

*Therefore, 6021 is not divisible by 7.*

(v)14126

**Ans:** Clearly,( 1412- 2 x 6)= 1400. Which is divisible by 7.

*Therefore, 14126 is divisible by 7.*

(vi)25368

**Ans:** Clearly, (2536-2 x 8)= 2520. Which is divisible by 7.

*Therefore, 25368 is divisible by 7.*

**7. Test the divisibility of the following numbers by 8:**

(i) 9364

**Ans: **The number formed by hundreds, ten and ones digits is 364. Which is clearly not divisible by 8.

*Therefore, 9364 is not divisible by 8.*

(ii) 2138

**Ans:** The number formed by hundreds, ten and ones digits is 138. Which is clearly not divisible by 8.

*Therefore, 2138 is not divisible by 8.*

(iii) 36792

**Ans:** The number formed by hundreds, ten and ones digits is 792. Which is clearly divisible by 8.

*Therefore, 36792 is divisible by 8.*

(iv) 901674

**Ans:** The number formed by hundreds, ten and ones digits is 674. Which is clearly not divisible by 8.

*Therefore, 901674 is not divisible by 8.*

(v) 136976

**Ans:** The number formed by hundreds, ten and ones digits is 976. Which is clearly divisible by 8.

*Therefore, 136976 is divisible by 8.*

(vi) 1790184

**Ans:** The number formed by hundreds, ten and ones digits is 184. Which is clearly divisible by 8.

*Therefore, 1790184 is divisible by 8.*

**8. Test the divisibility of the following numbers by 9:**

(i) 2358

**Ans:** Sum of the digits= (2+ 3+ 5 +8)= 18, Which is divisible by 9.

*Therefore, 2358 is divisible by 9.*

(ii) 3333

**Ans:** Sum of the digits= ( 3+ 3+ 3 +3)= 12, Which is not divisible by 9.

*Therefore, 3333 is not divisible by 9.*

(iii) 98712

**Ans:** Sum of the digits= (9+ 8 +7+ 1+ 2)= 27, Which is divisible by 9.

*Therefore, 98712 is divisible by 9.*

(iv) 257106

**Ans:** Sum of the digits= (2+ 5+ 7+ 1+ 0+ 6)= 21, Which is not divisible by 9.

*Therefore, 257106 is not divisible by 9.*

(v) 647514

**Ans:** Sum of the digits= (6+ 4+ 7+ 5+ 1+ 4)= 27, Which is divisible by 9.

*Therefore, 647514 is divisible by 9.*

(vi)326999

**Ans:** Sum of the digits= (3+ 2+ 6+ 9+ 9+ 9)= 38, Which is not divisible by 9.

*Therefore, 326999 is not divisible by 9.*

**9. Test the divisibility of the following numbers by 10:**

(i) 5790

**Ans:** Here 5790 is divisible by 10. Because the last digit is 0.

(ii) 63215

**Ans:** Here 63215 is not divisible by 10. Because the last digit is 5.

(iii) 55555

**Ans:** Here 55555 is not divisible by 10. Because the last digit is 5.

**10. Test the divisibility of the following numbers by 1****1:**

(i) 4334

**Ans:** 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, Which is divisible by 11.*

*Therefore, 4334 is divisible by 11.*

(ii) 83721

**Ans**: Sum of its digits in odd places=( 8+ 7+ 1)= 16

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

*Difference of the two sums= (16-5)=11, Which is divisible by 11.*

*Therefore, 83721 is divisible by 11.*

(iii) 66311

**Ans:** Sum of its digits in odd places= ( 6+3+1)= 10

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

*Difference of the two sums= (10-7)= 3, Which is not divisible by 11.*

*Therefore, 66311 is not divisible by 11.*

(iv) 137269

**Ans:** Sum of its digits in odd places= (1+ 7+ 6)= 14

*Sum of its digits in even places= ( 3+ 2+ 9)= 14*

*Difference of the two sums= (14-14)=0, Which is divisible by 11.*

*Therefore, 137269 is divisible by 11.*

(v) 901351

**Ans:** Sum of its digits in odd places= (9+ 1+5)= 15

*Sum of its digits in even places= (0+ 3+ 1)= 4*

*Difference of the two sums= (15-4)=11, Which is divisible by 11.*

*Therefore, 901351 is divisible by 11.*

(vi) 8790322

**Ans:** Sum of its digits in odd places= (8+ 9+ 3+ 2)= 22

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

*Difference of the two sums= (22-9)=13, Which is not divisible by 11.*

*Therefore, 8790322 is not divisible by 11.*

**11. In each of the following numbers, replace * by the smallest number to make it divisible by 3:**

(i) 27*4

= 2

(ii) 53*46

= 0

(iii) 8*711

= 1

(iv) 62*35

= 2

(v) 237*17

= 1

(vi)6*1054

= 2

**12. In each of the following numbers, replace * by the smallest number to make it divisible by 9:**

(i) 65*5

= 2

(ii) 2*135

= 7

(iii) 6702*

= 3

(iv) 91*67

= 4

(v) 6678*1

= 8

(vi) 835*86

= 6

**13. In each of the following numbers, replace * by the smallest number to make it divisible by 11:**

(i) 26*5

= 9

(ii) 39*43

= 7

(iii) 86*72

= 3

(iv) 467*91

= 2

(v) 1723*4

= 0

(vi)9*8071

= 1

**14. Test the divisibility of:**

(i) 10000001 by 11

**Ans:** 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, Which is divisible by 11.*

*Therefore, 10000001 is divisible by 11.*

(ii) 19083625 by 11

**Ans:** Sum of its digits in odd places= (1+ 0+ 3+ 2)= 6

*Sum of its digits in even places= ( 9+ 8+ 6+ 5)= 28*

*Difference of the two sums= (28- 6)= 22, Which is divisible by 11.*

*Therefore, 19083625 is divisible by 11.*

(iii) 2134563 by 9

**Ans:** Sum of the digits= (2+ 1+ 3+ 4+ 5+ 6+ 3)= 24, Which is not divisible by 9.

*Therefore, 2134563 is not divisible by 9.*

(iv) 10001001 by 3

**Ans:** Sum of the digits= (1+0+0+0+1+0+0+1)= 3, Which is divisible by 3.

*Therefore, 10001001 is divisible by 3.*

(v) 10203574 by 4

**Ans:** The number formed by the tens and ones digits is 74, which is not divisible by 4.

Therefore, 10203574 is not divisible by 4.

(vi) 12030624 by 8

**Ans:** The number formed by hundreds, ten and ones digits is 624. Which is clearly divisible by 8.

*Therefore, 12030624 is divisible by 8.*

**15. Which of the following are prime numbers?**

(i) 103

(ii) 137

(iii) 161

(iv) 179

(v) 217

(vi) 277

(vii) 331

(viii) 397

**Ans:** 103, 137, 179, 277, 331, 397 are prime numbers.

**Give an example of a number**

(i) Which is divisible by 2 but not by 4.

*Ans: 6*

(ii) Which is divisible by 4 but not by 8.

*Ans: 12*

(iii) Which is divisible by both 2 and 8 but not by 16.

*Ans: 24*

(iv) Which is divisible by both 3 and 6 but not by 18.

*Ans: 12*

**Write (T) for True and (F) for false against each of the following statement:**

(i) If a number is divisible by 4, it must be divisible by 8.

**Ans:** F

*Statement: When a number divisible by 4 if the number formed by its digits in the tens and ones place is divisible by 4 but the number is divisible by 8 if the number formed by its digits in hundreds, ten and one places is divisible by 8.*

(ii) If a number is divisible by 8, it must be divisible by 4.

**Ans:** T

(iii) If a number divides the sum of two numbers exactly, it must be divide the numbers separately.

**Ans:** F

*Statement: *

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

**Ans:** T

(v) A number is divisible by 18 if it is divisible by both 3 and 6.

**Ans:** F

*Statements: 3 and 6 are not co-primes. Consider 186.*

(vi) If a number is divisible by 3 and 7, it must be divisible by 21.

**Ans:** T

(vii) The sum of two consecutive odd numbers is always divisible by 4.

**Ans:** T

(viii)If a number divides two numbers exactly, it must divide their sum exactly.

**Ans:** T

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