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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 986 · 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 33330 divisible by 15?
  2. 2.Is 85080 divisible by 20?
  3. 3.Is 19805 divisible by 5?
  4. 4.Is 106970 divisible by 19?
  5. 5.Is 12774 divisible by 6?
  6. 6.Is 22701 divisible by 9?
  7. 7.Is 34047 divisible by 9?
  8. 8.Is 14587 divisible by 29?
  9. 9.Is 33881 divisible by 7?
  10. 10.Is 12350 divisible by 5?
  11. 11.Is 89233 divisible by 29?
  12. 12.Is 3860 divisible by 5?
  13. 13.Is 1755 divisible by 3?
  14. 14.Is 101064 divisible by 24?
  15. 15.Is 21957 divisible by 5?
  16. 16.Is 63453 divisible by 13?
  17. 17.Is 2897 divisible by 2?
  18. 18.Is 70544 divisible by 15?
  19. 19.Is 45920 divisible by 9?
  20. 20.Is 13209 divisible by 12?
  21. 21.Is 33870 divisible by 6?
  22. 22.Is 61952 divisible by 13?
  23. 23.Is 28182 divisible by 7?
  24. 24.Is 10380 divisible by 12?
  25. 25.Is 23093 divisible by 5?
  26. 26.Is 10649 divisible by 2?
  27. 27.Is 155304 divisible by 24?
  28. 28.Is 94335 divisible by 19?
  29. 29.Is 23261 divisible by 5?
  30. 30.Is 79885 divisible by 17?
  31. 31.Is 4248 divisible by 3?
  32. 32.Is 3170 divisible by 5?
  33. 33.Is 75956 divisible by 11?
  34. 34.Is 16956 divisible by 18?
  35. 35.Is 47364 divisible by 12?
  36. 36.Is 18612 divisible by 9?
  37. 37.Is 74426 divisible by 23?
  38. 38.Is 40919 divisible by 20?
  39. 39.Is 7827 divisible by 4?
  40. 40.Is 9409 divisible by 6?

Answer key

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

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