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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 758 · 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 5040 divisible by 5?
  2. 2.Is 10595 divisible by 9?
  3. 3.Is 65371 divisible by 10?
  4. 4.Is 50652 divisible by 9?
  5. 5.Is 18971 divisible by 19?
  6. 6.Is 27288 divisible by 17?
  7. 7.Is 15582 divisible by 6?
  8. 8.Is 5095 divisible by 4?
  9. 9.Is 84513 divisible by 13?
  10. 10.Is 6192 divisible by 2?
  11. 11.Is 19841 divisible by 5?
  12. 12.Is 2246 divisible by 2?
  13. 13.Is 30261 divisible by 11?
  14. 14.Is 13351 divisible by 13?
  15. 15.Is 44677 divisible by 20?
  16. 16.Is 7389 divisible by 10?
  17. 17.Is 65385 divisible by 20?
  18. 18.Is 142214 divisible by 24?
  19. 19.Is 17467 divisible by 8?
  20. 20.Is 6321 divisible by 5?
  21. 21.Is 59847 divisible by 17?
  22. 22.Is 145480 divisible by 29?
  23. 23.Is 40926 divisible by 8?
  24. 24.Is 79680 divisible by 15?
  25. 25.Is 62050 divisible by 10?
  26. 26.Is 98010 divisible by 18?
  27. 27.Is 51521 divisible by 15?
  28. 28.Is 202470 divisible by 30?
  29. 29.Is 3450 divisible by 5?
  30. 30.Is 10344 divisible by 6?
  31. 31.Is 25012 divisible by 13?
  32. 32.Is 20117 divisible by 5?
  33. 33.Is 2221 divisible by 7?
  34. 34.Is 20632 divisible by 12?
  35. 35.Is 50521 divisible by 19?
  36. 36.Is 14146 divisible by 7?
  37. 37.Is 29762 divisible by 6?
  38. 38.Is 22394 divisible by 4?
  39. 39.Is 98302 divisible by 23?
  40. 40.Is 11100 divisible by 19?

Answer key

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

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