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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 103 · 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 35465 divisible by 8?
  2. 2.Is 97404 divisible by 23?
  3. 3.Is 22390 divisible by 17?
  4. 4.Is 71394 divisible by 11?
  5. 5.Is 69359 divisible by 15?
  6. 6.Is 132317 divisible by 19?
  7. 7.Is 23667 divisible by 11?
  8. 8.Is 3658 divisible by 4?
  9. 9.Is 37981 divisible by 19?
  10. 10.Is 3096 divisible by 2?
  11. 11.Is 22719 divisible by 4?
  12. 12.Is 92309 divisible by 19?
  13. 13.Is 27999 divisible by 5?
  14. 14.Is 12567 divisible by 6?
  15. 15.Is 14290 divisible by 9?
  16. 16.Is 7230 divisible by 5?
  17. 17.Is 5200 divisible by 9?
  18. 18.Is 14164 divisible by 5?
  19. 19.Is 1055 divisible by 5?
  20. 20.Is 21353 divisible by 5?
  21. 21.Is 26430 divisible by 15?
  22. 22.Is 108180 divisible by 20?
  23. 23.Is 10620 divisible by 11?
  24. 24.Is 1385 divisible by 5?
  25. 25.Is 130110 divisible by 19?
  26. 26.Is 47730 divisible by 15?
  27. 27.Is 4686 divisible by 11?
  28. 28.Is 66618 divisible by 29?
  29. 29.Is 32660 divisible by 5?
  30. 30.Is 92124 divisible by 18?
  31. 31.Is 50402 divisible by 29?
  32. 32.Is 9568 divisible by 4?
  33. 33.Is 72661 divisible by 15?
  34. 34.Is 30240 divisible by 18?
  35. 35.Is 24271 divisible by 13?
  36. 36.Is 91306 divisible by 15?
  37. 37.Is 141979 divisible by 23?
  38. 38.Is 4091 divisible by 2?
  39. 39.Is 13476 divisible by 12?
  40. 40.Is 45857 divisible by 7?

Answer key

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

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