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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 902 · 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 38860 divisible by 20?
  2. 2.Is 44407 divisible by 11?
  3. 3.Is 3259 divisible by 3?
  4. 4.Is 38096 divisible by 8?
  5. 5.Is 63938 divisible by 10?
  6. 6.Is 17352 divisible by 8?
  7. 7.Is 147751 divisible by 29?
  8. 8.Is 111285 divisible by 18?
  9. 9.Is 18940 divisible by 20?
  10. 10.Is 78340 divisible by 20?
  11. 11.Is 112960 divisible by 20?
  12. 12.Is 141909 divisible by 23?
  13. 13.Is 106892 divisible by 20?
  14. 14.Is 10641 divisible by 11?
  15. 15.Is 145842 divisible by 29?
  16. 16.Is 7304 divisible by 5?
  17. 17.Is 7757 divisible by 12?
  18. 18.Is 12474 divisible by 2?
  19. 19.Is 10689 divisible by 13?
  20. 20.Is 59549 divisible by 24?
  21. 21.Is 196326 divisible by 30?
  22. 22.Is 107046 divisible by 19?
  23. 23.Is 131096 divisible by 19?
  24. 24.Is 58942 divisible by 13?
  25. 25.Is 63729 divisible by 11?
  26. 26.Is 26184 divisible by 10?
  27. 27.Is 12167 divisible by 2?
  28. 28.Is 57105 divisible by 10?
  29. 29.Is 32554 divisible by 29?
  30. 30.Is 40712 divisible by 8?
  31. 31.Is 3122 divisible by 2?
  32. 32.Is 183182 divisible by 30?
  33. 33.Is 31253 divisible by 23?
  34. 34.Is 41768 divisible by 10?
  35. 35.Is 59397 divisible by 13?
  36. 36.Is 23200 divisible by 20?
  37. 37.Is 4473 divisible by 7?
  38. 38.Is 132840 divisible by 30?
  39. 39.Is 28008 divisible by 9?
  40. 40.Is 76824 divisible by 29?

Answer key

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

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