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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 390 · 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 7705 divisible by 23?
  2. 2.Is 30840 divisible by 6?
  3. 3.Is 13249 divisible by 2?
  4. 4.Is 16092 divisible by 5?
  5. 5.Is 73758 divisible by 15?
  6. 6.Is 60567 divisible by 11?
  7. 7.Is 8288 divisible by 12?
  8. 8.Is 5360 divisible by 13?
  9. 9.Is 14999 divisible by 4?
  10. 10.Is 11030 divisible by 3?
  11. 11.Is 12228 divisible by 18?
  12. 12.Is 10847 divisible by 8?
  13. 13.Is 2035 divisible by 5?
  14. 14.Is 71709 divisible by 24?
  15. 15.Is 74988 divisible by 12?
  16. 16.Is 29734 divisible by 5?
  17. 17.Is 19584 divisible by 12?
  18. 18.Is 8552 divisible by 4?
  19. 19.Is 161385 divisible by 29?
  20. 20.Is 4283 divisible by 5?
  21. 21.Is 3750 divisible by 30?
  22. 22.Is 91596 divisible by 17?
  23. 23.Is 78823 divisible by 12?
  24. 24.Is 8331 divisible by 9?
  25. 25.Is 16195 divisible by 12?
  26. 26.Is 16240 divisible by 6?
  27. 27.Is 10190 divisible by 10?
  28. 28.Is 34983 divisible by 7?
  29. 29.Is 6568 divisible by 5?
  30. 30.Is 3092 divisible by 4?
  31. 31.Is 163038 divisible by 29?
  32. 32.Is 173430 divisible by 30?
  33. 33.Is 14769 divisible by 9?
  34. 34.Is 6581 divisible by 5?
  35. 35.Is 74508 divisible by 15?
  36. 36.Is 4958 divisible by 3?
  37. 37.Is 2646 divisible by 6?
  38. 38.Is 59685 divisible by 15?
  39. 39.Is 27828 divisible by 18?
  40. 40.Is 38074 divisible by 24?

Answer key

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

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