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

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 11:

(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

 


1 Comment

Add a Comment

Leave a Reply

Your email address will not be published.