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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 973 · 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 2952 divisible by 24?
  2. 2.Is 40851 divisible by 6?
  3. 3.Is 79971 divisible by 23?
  4. 4.Is 9237 divisible by 2?
  5. 5.Is 54300 divisible by 10?
  6. 6.Is 5103 divisible by 9?
  7. 7.Is 47191 divisible by 7?
  8. 8.Is 82593 divisible by 19?
  9. 9.Is 30240 divisible by 7?
  10. 10.Is 13201 divisible by 2?
  11. 11.Is 62447 divisible by 11?
  12. 12.Is 130773 divisible by 23?
  13. 13.Is 73756 divisible by 20?
  14. 14.Is 158064 divisible by 29?
  15. 15.Is 54540 divisible by 10?
  16. 16.Is 4162 divisible by 6?
  17. 17.Is 32655 divisible by 7?
  18. 18.Is 15301 divisible by 13?
  19. 19.Is 200014 divisible by 29?
  20. 20.Is 28842 divisible by 23?
  21. 21.Is 80253 divisible by 23?
  22. 22.Is 689 divisible by 19?
  23. 23.Is 13768 divisible by 8?
  24. 24.Is 50878 divisible by 23?
  25. 25.Is 17880 divisible by 30?
  26. 26.Is 3393 divisible by 9?
  27. 27.Is 17290 divisible by 10?
  28. 28.Is 65926 divisible by 10?
  29. 29.Is 7042 divisible by 18?
  30. 30.Is 140884 divisible by 30?
  31. 31.Is 111164 divisible by 20?
  32. 32.Is 2880 divisible by 24?
  33. 33.Is 43181 divisible by 29?
  34. 34.Is 43464 divisible by 7?
  35. 35.Is 22646 divisible by 13?
  36. 36.Is 3928 divisible by 6?
  37. 37.Is 45274 divisible by 23?
  38. 38.Is 15878 divisible by 17?
  39. 39.Is 48606 divisible by 17?
  40. 40.Is 6872 divisible by 13?

Answer key

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

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