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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 90 · 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 15862 divisible by 4?
  2. 2.Is 9282 divisible by 17?
  3. 3.Is 40122 divisible by 6?
  4. 4.Is 4916 divisible by 23?
  5. 5.Is 110181 divisible by 19?
  6. 6.Is 18029 divisible by 11?
  7. 7.Is 123372 divisible by 19?
  8. 8.Is 170636 divisible by 29?
  9. 9.Is 17535 divisible by 15?
  10. 10.Is 1207 divisible by 3?
  11. 11.Is 7428 divisible by 3?
  12. 12.Is 45945 divisible by 15?
  13. 13.Is 17350 divisible by 4?
  14. 14.Is 101808 divisible by 18?
  15. 15.Is 29013 divisible by 29?
  16. 16.Is 37538 divisible by 7?
  17. 17.Is 181343 divisible by 30?
  18. 18.Is 9797 divisible by 10?
  19. 19.Is 16026 divisible by 10?
  20. 20.Is 74129 divisible by 23?
  21. 21.Is 11258 divisible by 13?
  22. 22.Is 25908 divisible by 4?
  23. 23.Is 10061 divisible by 5?
  24. 24.Is 55368 divisible by 9?
  25. 25.Is 7432 divisible by 3?
  26. 26.Is 26568 divisible by 10?
  27. 27.Is 1239 divisible by 7?
  28. 28.Is 6970 divisible by 10?
  29. 29.Is 1343 divisible by 15?
  30. 30.Is 44221 divisible by 30?
  31. 31.Is 150995 divisible by 23?
  32. 32.Is 25556 divisible by 17?
  33. 33.Is 100419 divisible by 17?
  34. 34.Is 27172 divisible by 12?
  35. 35.Is 3542 divisible by 3?
  36. 36.Is 43838 divisible by 9?
  37. 37.Is 16216 divisible by 9?
  38. 38.Is 119380 divisible by 20?
  39. 39.Is 11592 divisible by 24?
  40. 40.Is 67106 divisible by 29?

Answer key

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

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