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

  1. 9572
  2. 81756
  3. 258671
  4. 672588
  5. 105756
  6. 269784

Answer:

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

  1.  81756
    • Sum of 8 + 1 + 7 + 5 + 6 = 27. 27 is divisible by 3. Hence 81756 is divisible by 3.
  2.  258671
    • Sum of 2 + 5 + 8 + 6 + 7 + 1 = 29. 29 is not divisible by 3. Hence 258671 is divisible by 3.
  3. 672588
    • Sum of 6 + 7 + 2 + 5 + 8 + 8 = 36. 36 is divisible by 3. Hence 672588 is divisible by 3.
  4.  105756
    • Sum of 1 + 0 + 5 + 7 + 5 + 6 = 24. 24 is divisible by 3. Hence 105756 is divisible by 3.
  5.  269784
    • 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?

  1. 971234
  2. 16524
  3. 382545
  4. 52618
  5. 843072
  6. 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.
  1. 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.
  2.  16524
    • Sum of 1 + 6 + 5 + 2 + 4 = 18. 18 is divisible both by 2 and 3. Hence the number is also divisible by 6.
  3.  382545
    • 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.
  4.  52618
    • 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.
  5.  843072
    • Sum of 8 + 4 + 3 + 0 + 7 + 2 = 24. 24 is divisible by 2 and 3. Hence the number is also divisible by 6.
  6.  64128
    • 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?

  1. 5714
  2. 29546
  3. 39784
  4. 64218
  5. 53876
  6. 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
  1. 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.
  2. 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.
  3.  39784
    • 84 is divisible by 4. Hence the 39784 is divisible by 4.
    • 784 is divisible by 8. Hence the 39784 is divisible by 8.
  4.  64218
    • 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.
  5.  53876
    • 76 is divisible by 4. Hence the 53876 is divisible by 4.
    • 876 is divisible by 8. Hence the 53876 is divisible by 8.
  6.  736912
    • 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?

  1. 95823
  2. 723618
  3. 36912
  4. 464646
  5. 183627
  6. 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.
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  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?

  1. 95827
  2. 110111
  3. 346929
  4. 517633
  5. 357269
  6. 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.

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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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