Q1. Using the test of divisibility, find which of the following numbers are divisible by 3?

- 9572
- 81756
- 258671
- 672588
- 105756
- 269784

Answer:

*Note: A number is divisible by 3, if the sum of the digits of the number is divisible by 3.*

*Sum of 8 + 1 + 7 + 5 + 6 = 27. 27 is divisible by 3. Hence 81756 is divisible by 3.*

*Sum of 2 + 5 + 8 + 6 + 7 + 1 = 29. 29 is not divisible by 3. Hence 258671 is divisible by 3*.

- 672588
*Sum of 6 + 7 + 2 + 5 + 8 + 8 = 36. 36 is divisible by 3. Hence 672588 is divisible by 3.*

*Sum of 1 + 0 + 5 + 7 + 5 + 6 = 24. 24 is divisible by 3. Hence 105756 is divisible by 3.*

*Sum of 2 + 6 + 9 + 7 + 8 + 4 = 36. 36 is divisible by 3. Hence 269784 is divisible by 3.*

Which of the above numbers are divisible by 9?

*Note: A number is divisible by 9 if the sum of the digits of the number is divisible by 9. *

*Therefore, 81756, 672588 and 269784 are divisible by 9.*

Q2. Using the test of divisibility, find which of the following numbers are divisible by 3?

- 971234
- 16524
- 382545
- 52618
- 843072
- 64128

Which of the above numbers are divisible by 6?

Answer:

*Note: A number is divisible by 3, if the sum of the digits of the number is divisible by 3.**Note: A number is divisible by 2, if the last digit of the number is 0, 2, 4, 6, and 8.**Note: A number is divisible by 6, if it is divisible both by 2 and 3.*

- 971234
*Sum of 9 + 7 + 1 + 2 + 3 + 4 = 26. 26 is not divisible by 3. Hence 971234 is not divisible by 3. It is divisible by 2.*

*Sum of 1 + 6 + 5 + 2 + 4 = 18. 18 is divisible both by 2 and 3. Hence the number is also divisible by 6.*

*Sum of 3 + 8 + 2 + 5 + 4 + 5 = 27. 27 is divisible by 3 but not by 2. Hence the number is not divisible by 6.*

*Sum of 5 + 2 + 6 + 1 + 8 = 22. 22 is divisible by 2 but not by 3. Hence the number is not divisible by 6.*

*Sum of 8 + 4 + 3 + 0 + 7 + 2 = 24. 24 is divisible by 2 and 3. Hence the number is also divisible by 6.*

*Sum of 6 + 4 + 1 + 2 + 8 = 21. 21 is divisible by 3 but not by 2. Hence the number is not divisible by 6.*

Q3. Using the test of divisibility, find which of the following numbers are divisible by 4?

- 5714
- 29546
- 39784
- 64218
- 53876
- 736912

Which of the above numbers are divisible by 8?

Answer:

*Note: *

*A number is divisible by 4 if the number formed by the last two digits of the number is divisible by 4.**A number is divisible by 8 if the number formed by then last three digits of the number is divisible by 8*

- 5714
- 14 is not divisible by 4. Hence the 5714 is not divisible by 4.
- 714 is not divisible by 8. Hence the 5714 is not divisible by 8.

- 29546
- 46 is not divisible by 4. Hence the 29546 is not divisible by 4.
- 546 is not divisible by 8. Hence the 29546 is not divisible by 8.

*84 is divisible by 4. Hence the 39784 is divisible by 4.**784 is divisible by 8. Hence the 39784 is divisible by 8.*

*18 is not divisible by 4. Hence the 64218 is not divisible by 4.**218 is not divisible by 8. Hence the 64218 is not divisible by 8.*

*76 is divisible by 4. Hence the 53876 is divisible by 4.**876 is divisible by 8. Hence the 53876 is divisible by 8.*

*12 is divisible by 4. Hence the 736912 is divisible by 4.**912 is divisible by 8. Hence the 736912 is divisible by 8.*

Q4. Which of the above numbers are divisible by 6?

- 95823
- 723618
- 36912
- 464646
- 183627
- 341296

Answer:

*Note:*

*A number is divisible by 3, if the sum of the digits of the number is divisible by 3.**A number is divisible by 2, if the last digit of the number is 0, 2, 4, 6, and 8.**A number is divisible by 6, if it is divisible both by 2 and 3.*

- 95823
*Sum of 9 + 5 + 8 + 2 + 3 = 27. 27 is divisible by 3. Hence 95823 is divisible by 3.**The last digit is 3 which is not divisible by 2.**Hence the number is not divisible by 6.*

- 723618
*Sum of 7 + 2 + 3 + 6 + 1 + 8 = 27. 27 is divisible by 3. Hence 723618 is divisible by 3.**The last digit is 8 which is divisible by 2.**Hence the number is divisible by 6.*

- 36912
*Sum of 3 + 6 + 9 + 1 + 2 = 21. 21 is divisible by 3. Hence 36912 is divisible by 3.**The last digit is 2 which is divisible by 2.**Hence the number is divisible by 6.*

- 464646
*Sum of 4 + 6 + 4 + 6 + 4 + 6 = 30. 30 is divisible by 3. Hence 464646 is divisible by 3.**The last digit is 6 which is divisible by 2.**Hence the number is divisible by 6.*

- 183627
*Sum of 1 + 8 + 3 + 6 + 2 + 7 = 27. 27 is divisible by 3. Hence 183627 is divisible by 3.**The last digit is 7 which is not divisible by 2.**Hence the number is not divisible by 6.*

- 341296
*Sum of 3 + 4 + 1 + 2 + 9 + 6 = 25. 27 is not divisible by 3. Hence 341296 is divisible by 3.**The last digit is 3 which is not divisible by 2.**Hence the number is not divisible by 6.*

Q5. Which of the above numbers are divisible by 11?

- 95827
- 110111
- 346929
- 517633
- 357269
- 5245185

Answer:

*Note: A number is divisible by 11 id the difference between the sum of its digits at odd places and the sum of the digits at even places is either 0 or a number divisible by 11.*

- 95827
*Difference = (sum of digits at odd places) – (sum of digits at even places)**= (7 + 8 + 9) – (2 + 5) = 24 – 7 = 17.**17 is not divisible by 11. Hence then number is not divisible by 11.*

- 110111
*Difference = (sum of digits at odd places) – (sum of digits at even places)**= (1 + 1 + 1) – (1+0 +1) = 3 – 1 = 1.**1 is not divisible by 11. Hence then number is not divisible by 11.*

- 346929
*Difference = (sum of digits at odd places) – (sum of digits at even places)**= (9 + 9 + 4) – (2 + 6 + 3) = 22 – 11 = 11.**11 is divisible by 11. Hence then number is divisible by 11.*

- 517633
*Difference = (sum of digits at odd places) – (sum of digits at even places)**= (3 + 6 + 1) – (3 + 7 + 5) = 10 – 15 = -5.**-5 is no divisible by 11. Hence then number is not divisible by 11.*

- 357269
*Difference = (sum of digits at odd places) – (sum of digits at even places)**= (9 + 2 + 5) – (6 + 7 + 3) = 16 – 16 = 0.**Hence then number is divisible by 11.*

- 5245185
*Difference = (sum of digits at odd places) – (sum of digits at even places)**= (5 + 1 + 4 + 5) – (8 + 5 + 2) = 15 – 15 = 0.**Hence then number is divisible by 11.*

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