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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 988 · 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 119661 divisible by 29?
  2. 2.Is 3051 divisible by 3?
  3. 3.Is 8120 divisible by 20?
  4. 4.Is 32952 divisible by 12?
  5. 5.Is 85605 divisible by 13?
  6. 6.Is 18969 divisible by 10?
  7. 7.Is 36503 divisible by 6?
  8. 8.Is 48851 divisible by 11?
  9. 9.Is 46031 divisible by 30?
  10. 10.Is 10440 divisible by 12?
  11. 11.Is 34596 divisible by 18?
  12. 12.Is 40515 divisible by 6?
  13. 13.Is 148440 divisible by 30?
  14. 14.Is 57893 divisible by 19?
  15. 15.Is 18757 divisible by 3?
  16. 16.Is 32496 divisible by 19?
  17. 17.Is 3330 divisible by 3?
  18. 18.Is 23352 divisible by 7?
  19. 19.Is 12133 divisible by 6?
  20. 20.Is 23605 divisible by 8?
  21. 21.Is 12369 divisible by 3?
  22. 22.Is 5365 divisible by 4?
  23. 23.Is 8042 divisible by 3?
  24. 24.Is 28870 divisible by 12?
  25. 25.Is 55945 divisible by 10?
  26. 26.Is 95407 divisible by 17?
  27. 27.Is 8286 divisible by 3?
  28. 28.Is 183007 divisible by 30?
  29. 29.Is 1376 divisible by 4?
  30. 30.Is 18231 divisible by 4?
  31. 31.Is 53430 divisible by 30?
  32. 32.Is 91433 divisible by 19?
  33. 33.Is 16560 divisible by 6?
  34. 34.Is 134460 divisible by 20?
  35. 35.Is 23504 divisible by 4?
  36. 36.Is 1650 divisible by 11?
  37. 37.Is 21948 divisible by 4?
  38. 38.Is 4506 divisible by 2?
  39. 39.Is 4994 divisible by 7?
  40. 40.Is 34294 divisible by 13?

Answer key

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

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