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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 692 · 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 23202 divisible by 6?
  2. 2.Is 5345 divisible by 5?
  3. 3.Is 110700 divisible by 20?
  4. 4.Is 2616 divisible by 6?
  5. 5.Is 21097 divisible by 17?
  6. 6.Is 2244 divisible by 17?
  7. 7.Is 24960 divisible by 13?
  8. 8.Is 55955 divisible by 8?
  9. 9.Is 40048 divisible by 19?
  10. 10.Is 131109 divisible by 29?
  11. 11.Is 698 divisible by 3?
  12. 12.Is 1471 divisible by 2?
  13. 13.Is 13889 divisible by 2?
  14. 14.Is 141036 divisible by 23?
  15. 15.Is 8786 divisible by 23?
  16. 16.Is 51759 divisible by 9?
  17. 17.Is 63606 divisible by 15?
  18. 18.Is 484 divisible by 11?
  19. 19.Is 80308 divisible by 17?
  20. 20.Is 26891 divisible by 4?
  21. 21.Is 181980 divisible by 30?
  22. 22.Is 55920 divisible by 30?
  23. 23.Is 87160 divisible by 20?
  24. 24.Is 7353 divisible by 15?
  25. 25.Is 1550 divisible by 19?
  26. 26.Is 136846 divisible by 20?
  27. 27.Is 10365 divisible by 30?
  28. 28.Is 32452 divisible by 5?
  29. 29.Is 188421 divisible by 29?
  30. 30.Is 35858 divisible by 6?
  31. 31.Is 81459 divisible by 23?
  32. 32.Is 64497 divisible by 17?
  33. 33.Is 309 divisible by 2?
  34. 34.Is 35529 divisible by 13?
  35. 35.Is 116130 divisible by 19?
  36. 36.Is 159670 divisible by 23?
  37. 37.Is 10871 divisible by 2?
  38. 38.Is 23809 divisible by 6?
  39. 39.Is 23383 divisible by 12?
  40. 40.Is 70164 divisible by 20?

Answer key

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

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