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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 603 · 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 119681 divisible by 19?
  2. 2.Is 101551 divisible by 19?
  3. 3.Is 13021 divisible by 5?
  4. 4.Is 27919 divisible by 8?
  5. 5.Is 1625 divisible by 6?
  6. 6.Is 149088 divisible by 24?
  7. 7.Is 17318 divisible by 7?
  8. 8.Is 61028 divisible by 19?
  9. 9.Is 75491 divisible by 13?
  10. 10.Is 32121 divisible by 20?
  11. 11.Is 91746 divisible by 18?
  12. 12.Is 6456 divisible by 6?
  13. 13.Is 29280 divisible by 30?
  14. 14.Is 119963 divisible by 23?
  15. 15.Is 68775 divisible by 24?
  16. 16.Is 46753 divisible by 7?
  17. 17.Is 90339 divisible by 23?
  18. 18.Is 25621 divisible by 13?
  19. 19.Is 861 divisible by 11?
  20. 20.Is 59568 divisible by 24?
  21. 21.Is 21146 divisible by 4?
  22. 22.Is 995 divisible by 5?
  23. 23.Is 39098 divisible by 7?
  24. 24.Is 67914 divisible by 18?
  25. 25.Is 105480 divisible by 30?
  26. 26.Is 9763 divisible by 15?
  27. 27.Is 131573 divisible by 29?
  28. 28.Is 84629 divisible by 17?
  29. 29.Is 340 divisible by 4?
  30. 30.Is 106440 divisible by 20?
  31. 31.Is 42285 divisible by 15?
  32. 32.Is 30540 divisible by 8?
  33. 33.Is 13153 divisible by 9?
  34. 34.Is 40252 divisible by 29?
  35. 35.Is 16750 divisible by 4?
  36. 36.Is 59611 divisible by 23?
  37. 37.Is 54903 divisible by 9?
  38. 38.Is 28781 divisible by 17?
  39. 39.Is 4707 divisible by 3?
  40. 40.Is 18052 divisible by 6?

Answer key

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

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