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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 851 · 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 18014 divisible by 3?
  2. 2.Is 45595 divisible by 8?
  3. 3.Is 55180 divisible by 18?
  4. 4.Is 6110 divisible by 10?
  5. 5.Is 134096 divisible by 29?
  6. 6.Is 10723 divisible by 2?
  7. 7.Is 54108 divisible by 8?
  8. 8.Is 970 divisible by 5?
  9. 9.Is 9591 divisible by 5?
  10. 10.Is 29400 divisible by 18?
  11. 11.Is 7405 divisible by 2?
  12. 12.Is 11487 divisible by 7?
  13. 13.Is 101781 divisible by 20?
  14. 14.Is 89697 divisible by 29?
  15. 15.Is 11818 divisible by 3?
  16. 16.Is 43714 divisible by 10?
  17. 17.Is 12146 divisible by 7?
  18. 18.Is 3420 divisible by 30?
  19. 19.Is 1458 divisible by 6?
  20. 20.Is 114886 divisible by 23?
  21. 21.Is 48484 divisible by 23?
  22. 22.Is 19443 divisible by 6?
  23. 23.Is 29828 divisible by 12?
  24. 24.Is 113756 divisible by 24?
  25. 25.Is 47581 divisible by 19?
  26. 26.Is 7005 divisible by 2?
  27. 27.Is 12181 divisible by 3?
  28. 28.Is 39005 divisible by 6?
  29. 29.Is 8683 divisible by 8?
  30. 30.Is 30320 divisible by 9?
  31. 31.Is 93540 divisible by 15?
  32. 32.Is 507 divisible by 13?
  33. 33.Is 33111 divisible by 9?
  34. 34.Is 19947 divisible by 5?
  35. 35.Is 24701 divisible by 17?
  36. 36.Is 27050 divisible by 24?
  37. 37.Is 47760 divisible by 30?
  38. 38.Is 53700 divisible by 10?
  39. 39.Is 28710 divisible by 29?
  40. 40.Is 8480 divisible by 8?

Answer key

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

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