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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 680 · 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 1283 divisible by 11?
  2. 2.Is 140 divisible by 2?
  3. 3.Is 10301 divisible by 9?
  4. 4.Is 21574 divisible by 7?
  5. 5.Is 17713 divisible by 15?
  6. 6.Is 14652 divisible by 3?
  7. 7.Is 83356 divisible by 13?
  8. 8.Is 33408 divisible by 9?
  9. 9.Is 23047 divisible by 8?
  10. 10.Is 117363 divisible by 29?
  11. 11.Is 50829 divisible by 9?
  12. 12.Is 148772 divisible by 29?
  13. 13.Is 9748 divisible by 5?
  14. 14.Is 3420 divisible by 30?
  15. 15.Is 150477 divisible by 24?
  16. 16.Is 590 divisible by 7?
  17. 17.Is 19484 divisible by 8?
  18. 18.Is 18279 divisible by 13?
  19. 19.Is 2700 divisible by 18?
  20. 20.Is 30026 divisible by 6?
  21. 21.Is 58130 divisible by 24?
  22. 22.Is 4284 divisible by 4?
  23. 23.Is 40950 divisible by 18?
  24. 24.Is 30511 divisible by 6?
  25. 25.Is 34136 divisible by 8?
  26. 26.Is 3792 divisible by 6?
  27. 27.Is 75808 divisible by 23?
  28. 28.Is 65909 divisible by 11?
  29. 29.Is 91324 divisible by 17?
  30. 30.Is 157230 divisible by 30?
  31. 31.Is 1380 divisible by 7?
  32. 32.Is 32568 divisible by 6?
  33. 33.Is 2622 divisible by 3?
  34. 34.Is 94561 divisible by 29?
  35. 35.Is 36158 divisible by 10?
  36. 36.Is 94444 divisible by 20?
  37. 37.Is 91162 divisible by 19?
  38. 38.Is 53899 divisible by 23?
  39. 39.Is 49979 divisible by 9?
  40. 40.Is 35423 divisible by 8?

Answer key

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

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