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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 124 · 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 107156 divisible by 19?
  2. 2.Is 131713 divisible by 30?
  3. 3.Is 3974 divisible by 2?
  4. 4.Is 5075 divisible by 29?
  5. 5.Is 94151 divisible by 30?
  6. 6.Is 3347 divisible by 6?
  7. 7.Is 57744 divisible by 18?
  8. 8.Is 87239 divisible by 13?
  9. 9.Is 851 divisible by 6?
  10. 10.Is 12575 divisible by 7?
  11. 11.Is 40475 divisible by 8?
  12. 12.Is 142944 divisible by 24?
  13. 13.Is 12856 divisible by 4?
  14. 14.Is 103986 divisible by 18?
  15. 15.Is 7488 divisible by 6?
  16. 16.Is 35450 divisible by 9?
  17. 17.Is 44711 divisible by 23?
  18. 18.Is 84591 divisible by 18?
  19. 19.Is 9096 divisible by 24?
  20. 20.Is 19711 divisible by 18?
  21. 21.Is 49450 divisible by 10?
  22. 22.Is 10344 divisible by 2?
  23. 23.Is 28195 divisible by 9?
  24. 24.Is 1487 divisible by 24?
  25. 25.Is 59160 divisible by 24?
  26. 26.Is 12448 divisible by 8?
  27. 27.Is 155549 divisible by 23?
  28. 28.Is 10275 divisible by 15?
  29. 29.Is 155384 divisible by 24?
  30. 30.Is 15496 divisible by 13?
  31. 31.Is 35152 divisible by 23?
  32. 32.Is 150624 divisible by 24?
  33. 33.Is 32294 divisible by 5?
  34. 34.Is 25312 divisible by 8?
  35. 35.Is 24108 divisible by 7?
  36. 36.Is 43766 divisible by 11?
  37. 37.Is 55781 divisible by 9?
  38. 38.Is 80064 divisible by 18?
  39. 39.Is 135512 divisible by 24?
  40. 40.Is 40446 divisible by 9?

Answer key

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

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