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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 168 · 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 74864 divisible by 13?
  2. 2.Is 39727 divisible by 20?
  3. 3.Is 7633 divisible by 6?
  4. 4.Is 52680 divisible by 30?
  5. 5.Is 15708 divisible by 12?
  6. 6.Is 40612 divisible by 10?
  7. 7.Is 11713 divisible by 4?
  8. 8.Is 30219 divisible by 13?
  9. 9.Is 7415 divisible by 7?
  10. 10.Is 181478 divisible by 30?
  11. 11.Is 9298 divisible by 12?
  12. 12.Is 23987 divisible by 5?
  13. 13.Is 194619 divisible by 29?
  14. 14.Is 191258 divisible by 30?
  15. 15.Is 14912 divisible by 11?
  16. 16.Is 1610 divisible by 5?
  17. 17.Is 34257 divisible by 19?
  18. 18.Is 15041 divisible by 3?
  19. 19.Is 3084 divisible by 3?
  20. 20.Is 16175 divisible by 5?
  21. 21.Is 108566 divisible by 19?
  22. 22.Is 56526 divisible by 23?
  23. 23.Is 75720 divisible by 30?
  24. 24.Is 185832 divisible by 30?
  25. 25.Is 9340 divisible by 20?
  26. 26.Is 39934 divisible by 19?
  27. 27.Is 83551 divisible by 12?
  28. 28.Is 18552 divisible by 24?
  29. 29.Is 53316 divisible by 9?
  30. 30.Is 21947 divisible by 7?
  31. 31.Is 17895 divisible by 3?
  32. 32.Is 26472 divisible by 24?
  33. 33.Is 51948 divisible by 9?
  34. 34.Is 35813 divisible by 11?
  35. 35.Is 152112 divisible by 24?
  36. 36.Is 96552 divisible by 18?
  37. 37.Is 119032 divisible by 24?
  38. 38.Is 29822 divisible by 6?
  39. 39.Is 3959 divisible by 3?
  40. 40.Is 68844 divisible by 12?

Answer key

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

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