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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 359 · 40 sums
TalentJR

The trick (Ekadhikena Purvena): 2, 5, 10: the last digit (even; 0 or 5; 0). 3 and 9: add the digits. 4: the last two digits. 8: the last three digits. 6: even and passes the rule for 3. 11: from the right, add the 1st, 3rd, 5th… digits and the 2nd, 4th… digits; the difference must be 0 or a multiple of 11. Any prime p: multiply p by 1, 3, 7 or 9 so it ends in 9; one more than the digits before the 9 is the osculator (7 → 5, 13 → 4, 17 → 12, 19 → 2, 23 → 7, 29 → 3). Take the last digit × the osculator and add it to the rest; repeat until the number is small and check the times table. Composite numbers: split into two factors that share no factor and pass BOTH rules — 6 = 2 × 3, 12 = 3 × 4, 15 = 3 × 5, 18 = 2 × 9, 20 = 4 × 5, 24 = 3 × 8, 30 = 3 × 10.

NameDateTime takenScore ___ / 40
  1. 1.Is 124241 divisible by 19?
  2. 2.Is 352 divisible by 11?
  3. 3.Is 53685 divisible by 9?
  4. 4.Is 28355 divisible by 5?
  5. 5.Is 72486 divisible by 17?
  6. 6.Is 9767 divisible by 2?
  7. 7.Is 105685 divisible by 23?
  8. 8.Is 34998 divisible by 19?
  9. 9.Is 78252 divisible by 12?
  10. 10.Is 42414 divisible by 23?
  11. 11.Is 8830 divisible by 2?
  12. 12.Is 49966 divisible by 10?
  13. 13.Is 6175 divisible by 19?
  14. 14.Is 19475 divisible by 7?
  15. 15.Is 70955 divisible by 23?
  16. 16.Is 63357 divisible by 19?
  17. 17.Is 10121 divisible by 3?
  18. 18.Is 19634 divisible by 3?
  19. 19.Is 96603 divisible by 29?
  20. 20.Is 33943 divisible by 7?
  21. 21.Is 15440 divisible by 3?
  22. 22.Is 38131 divisible by 17?
  23. 23.Is 68149 divisible by 23?
  24. 24.Is 66413 divisible by 12?
  25. 25.Is 12430 divisible by 5?
  26. 26.Is 11561 divisible by 2?
  27. 27.Is 1577 divisible by 2?
  28. 28.Is 7176 divisible by 11?
  29. 29.Is 75371 divisible by 29?
  30. 30.Is 4718 divisible by 2?
  31. 31.Is 46760 divisible by 20?
  32. 32.Is 90077 divisible by 13?
  33. 33.Is 112143 divisible by 30?
  34. 34.Is 32006 divisible by 13?
  35. 35.Is 181604 divisible by 29?
  36. 36.Is 12600 divisible by 30?
  37. 37.Is 40122 divisible by 7?
  38. 38.Is 46996 divisible by 11?
  39. 39.Is 19950 divisible by 30?
  40. 40.Is 65733 divisible by 18?

Answer key

  1. yes
  2. yes
  3. yes
  4. yes
  5. no
  6. no
  7. yes
  8. yes
  9. yes
  10. no
  11. yes
  12. no
  13. yes
  14. no
  15. yes
  16. no
  17. no
  18. no
  19. no
  20. yes
  21. no
  22. yes
  23. yes
  24. no
  25. yes
  26. no
  27. no
  28. no
  29. yes
  30. yes
  31. yes
  32. yes
  33. no
  34. yes
  35. no
  36. yes
  37. no
  38. no
  39. yes
  40. no

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