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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 402 · 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 37365 divisible by 6?
  2. 2.Is 26820 divisible by 18?
  3. 3.Is 13196 divisible by 3?
  4. 4.Is 34045 divisible by 7?
  5. 5.Is 50310 divisible by 18?
  6. 6.Is 11336 divisible by 3?
  7. 7.Is 1057 divisible by 15?
  8. 8.Is 90417 divisible by 30?
  9. 9.Is 11001 divisible by 19?
  10. 10.Is 112140 divisible by 18?
  11. 11.Is 65104 divisible by 13?
  12. 12.Is 4781 divisible by 3?
  13. 13.Is 159548 divisible by 29?
  14. 14.Is 7956 divisible by 13?
  15. 15.Is 36389 divisible by 9?
  16. 16.Is 59455 divisible by 9?
  17. 17.Is 30180 divisible by 12?
  18. 18.Is 2696 divisible by 3?
  19. 19.Is 148658 divisible by 29?
  20. 20.Is 14179 divisible by 7?
  21. 21.Is 80931 divisible by 20?
  22. 22.Is 31716 divisible by 18?
  23. 23.Is 49554 divisible by 8?
  24. 24.Is 13334 divisible by 11?
  25. 25.Is 162662 divisible by 24?
  26. 26.Is 51842 divisible by 23?
  27. 27.Is 7047 divisible by 9?
  28. 28.Is 27788 divisible by 13?
  29. 29.Is 52112 divisible by 8?
  30. 30.Is 38946 divisible by 6?
  31. 31.Is 72929 divisible by 11?
  32. 32.Is 16050 divisible by 30?
  33. 33.Is 10708 divisible by 4?
  34. 34.Is 91750 divisible by 18?
  35. 35.Is 4778 divisible by 2?
  36. 36.Is 166926 divisible by 24?
  37. 37.Is 53795 divisible by 9?
  38. 38.Is 96202 divisible by 17?
  39. 39.Is 26566 divisible by 19?
  40. 40.Is 6824 divisible by 4?

Answer key

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

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