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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 262 · 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 5058 divisible by 2?
  2. 2.Is 31497 divisible by 11?
  3. 3.Is 7106 divisible by 17?
  4. 4.Is 12161 divisible by 2?
  5. 5.Is 180670 divisible by 29?
  6. 6.Is 35235 divisible by 15?
  7. 7.Is 494 divisible by 19?
  8. 8.Is 21358 divisible by 4?
  9. 9.Is 101338 divisible by 23?
  10. 10.Is 11222 divisible by 2?
  11. 11.Is 6599 divisible by 7?
  12. 12.Is 28600 divisible by 23?
  13. 13.Is 14384 divisible by 4?
  14. 14.Is 4425 divisible by 2?
  15. 15.Is 187732 divisible by 30?
  16. 16.Is 27768 divisible by 9?
  17. 17.Is 93393 divisible by 15?
  18. 18.Is 6947 divisible by 2?
  19. 19.Is 6818 divisible by 8?
  20. 20.Is 47448 divisible by 8?
  21. 21.Is 41090 divisible by 6?
  22. 22.Is 61250 divisible by 10?
  23. 23.Is 162418 divisible by 30?
  24. 24.Is 19728 divisible by 3?
  25. 25.Is 10410 divisible by 5?
  26. 26.Is 95862 divisible by 17?
  27. 27.Is 33534 divisible by 23?
  28. 28.Is 75966 divisible by 13?
  29. 29.Is 12389 divisible by 4?
  30. 30.Is 34903 divisible by 5?
  31. 31.Is 36982 divisible by 17?
  32. 32.Is 13240 divisible by 20?
  33. 33.Is 8256 divisible by 2?
  34. 34.Is 23002 divisible by 7?
  35. 35.Is 8728 divisible by 3?
  36. 36.Is 21384 divisible by 24?
  37. 37.Is 7212 divisible by 12?
  38. 38.Is 9988 divisible by 3?
  39. 39.Is 28020 divisible by 6?
  40. 40.Is 196700 divisible by 30?

Answer key

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

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