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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 949 · 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 124163 divisible by 18?
  2. 2.Is 44662 divisible by 11?
  3. 3.Is 40120 divisible by 17?
  4. 4.Is 10121 divisible by 7?
  5. 5.Is 38057 divisible by 9?
  6. 6.Is 102374 divisible by 17?
  7. 7.Is 16214 divisible by 3?
  8. 8.Is 23301 divisible by 17?
  9. 9.Is 90801 divisible by 13?
  10. 10.Is 57985 divisible by 10?
  11. 11.Is 33534 divisible by 9?
  12. 12.Is 147528 divisible by 24?
  13. 13.Is 30359 divisible by 7?
  14. 14.Is 37643 divisible by 23?
  15. 15.Is 80639 divisible by 12?
  16. 16.Is 26025 divisible by 5?
  17. 17.Is 4191 divisible by 5?
  18. 18.Is 65038 divisible by 29?
  19. 19.Is 18262 divisible by 24?
  20. 20.Is 44505 divisible by 23?
  21. 21.Is 7975 divisible by 29?
  22. 22.Is 24110 divisible by 15?
  23. 23.Is 11220 divisible by 30?
  24. 24.Is 7171 divisible by 10?
  25. 25.Is 55073 divisible by 8?
  26. 26.Is 58120 divisible by 20?
  27. 27.Is 20222 divisible by 3?
  28. 28.Is 21008 divisible by 4?
  29. 29.Is 77610 divisible by 13?
  30. 30.Is 27250 divisible by 5?
  31. 31.Is 8972 divisible by 3?
  32. 32.Is 121050 divisible by 19?
  33. 33.Is 48709 divisible by 18?
  34. 34.Is 71028 divisible by 12?
  35. 35.Is 9966 divisible by 10?
  36. 36.Is 52716 divisible by 12?
  37. 37.Is 46785 divisible by 9?
  38. 38.Is 15626 divisible by 3?
  39. 39.Is 36293 divisible by 11?
  40. 40.Is 108380 divisible by 20?

Answer key

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

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