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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 950 · 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 28089 divisible by 23?
  2. 2.Is 2749 divisible by 19?
  3. 3.Is 5163 divisible by 17?
  4. 4.Is 53176 divisible by 18?
  5. 5.Is 9048 divisible by 12?
  6. 6.Is 127186 divisible by 19?
  7. 7.Is 17015 divisible by 4?
  8. 8.Is 53460 divisible by 30?
  9. 9.Is 29524 divisible by 30?
  10. 10.Is 5793 divisible by 11?
  11. 11.Is 60340 divisible by 29?
  12. 12.Is 53924 divisible by 30?
  13. 13.Is 20118 divisible by 6?
  14. 14.Is 25760 divisible by 23?
  15. 15.Is 20634 divisible by 3?
  16. 16.Is 42717 divisible by 7?
  17. 17.Is 111891 divisible by 19?
  18. 18.Is 97221 divisible by 23?
  19. 19.Is 115173 divisible by 29?
  20. 20.Is 97584 divisible by 24?
  21. 21.Is 137520 divisible by 30?
  22. 22.Is 125670 divisible by 30?
  23. 23.Is 20355 divisible by 5?
  24. 24.Is 2253 divisible by 3?
  25. 25.Is 12277 divisible by 3?
  26. 26.Is 54201 divisible by 10?
  27. 27.Is 90678 divisible by 17?
  28. 28.Is 14282 divisible by 23?
  29. 29.Is 49836 divisible by 12?
  30. 30.Is 13344 divisible by 12?
  31. 31.Is 64667 divisible by 12?
  32. 32.Is 160563 divisible by 23?
  33. 33.Is 89733 divisible by 17?
  34. 34.Is 87628 divisible by 30?
  35. 35.Is 8881 divisible by 17?
  36. 36.Is 66880 divisible by 20?
  37. 37.Is 2720 divisible by 20?
  38. 38.Is 19900 divisible by 5?
  39. 39.Is 10212 divisible by 6?
  40. 40.Is 20561 divisible by 13?

Answer key

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

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