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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 559 · 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 6590 divisible by 2?
  2. 2.Is 3340 divisible by 2?
  3. 3.Is 79729 divisible by 13?
  4. 4.Is 53073 divisible by 11?
  5. 5.Is 64671 divisible by 19?
  6. 6.Is 9915 divisible by 4?
  7. 7.Is 14174 divisible by 3?
  8. 8.Is 154802 divisible by 29?
  9. 9.Is 42552 divisible by 12?
  10. 10.Is 119510 divisible by 19?
  11. 11.Is 23952 divisible by 15?
  12. 12.Is 41276 divisible by 19?
  13. 13.Is 160958 divisible by 23?
  14. 14.Is 152946 divisible by 24?
  15. 15.Is 25574 divisible by 19?
  16. 16.Is 52845 divisible by 15?
  17. 17.Is 28599 divisible by 7?
  18. 18.Is 22540 divisible by 5?
  19. 19.Is 39381 divisible by 9?
  20. 20.Is 2862 divisible by 3?
  21. 21.Is 3750 divisible by 6?
  22. 22.Is 35835 divisible by 6?
  23. 23.Is 39933 divisible by 29?
  24. 24.Is 39575 divisible by 17?
  25. 25.Is 72902 divisible by 15?
  26. 26.Is 11055 divisible by 5?
  27. 27.Is 34900 divisible by 11?
  28. 28.Is 60300 divisible by 20?
  29. 29.Is 90661 divisible by 17?
  30. 30.Is 2356 divisible by 15?
  31. 31.Is 41475 divisible by 29?
  32. 32.Is 65565 divisible by 15?
  33. 33.Is 35832 divisible by 8?
  34. 34.Is 67887 divisible by 13?
  35. 35.Is 106351 divisible by 19?
  36. 36.Is 23582 divisible by 4?
  37. 37.Is 24099 divisible by 29?
  38. 38.Is 67498 divisible by 18?
  39. 39.Is 40875 divisible by 12?
  40. 40.Is 74375 divisible by 29?

Answer key

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

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