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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 978 · 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 60709 divisible by 13?
  2. 2.Is 68010 divisible by 15?
  3. 3.Is 12395 divisible by 15?
  4. 4.Is 99013 divisible by 15?
  5. 5.Is 18570 divisible by 30?
  6. 6.Is 25444 divisible by 6?
  7. 7.Is 34435 divisible by 6?
  8. 8.Is 92781 divisible by 18?
  9. 9.Is 11191 divisible by 6?
  10. 10.Is 26180 divisible by 7?
  11. 11.Is 2610 divisible by 2?
  12. 12.Is 23018 divisible by 6?
  13. 13.Is 3919 divisible by 2?
  14. 14.Is 28277 divisible by 10?
  15. 15.Is 163480 divisible by 30?
  16. 16.Is 7525 divisible by 2?
  17. 17.Is 82980 divisible by 12?
  18. 18.Is 12745 divisible by 5?
  19. 19.Is 75418 divisible by 15?
  20. 20.Is 35597 divisible by 8?
  21. 21.Is 92436 divisible by 18?
  22. 22.Is 25329 divisible by 4?
  23. 23.Is 47585 divisible by 9?
  24. 24.Is 2317 divisible by 4?
  25. 25.Is 135935 divisible by 24?
  26. 26.Is 53808 divisible by 12?
  27. 27.Is 56430 divisible by 19?
  28. 28.Is 111499 divisible by 30?
  29. 29.Is 28176 divisible by 10?
  30. 30.Is 71680 divisible by 30?
  31. 31.Is 8260 divisible by 10?
  32. 32.Is 58004 divisible by 17?
  33. 33.Is 71297 divisible by 12?
  34. 34.Is 25453 divisible by 18?
  35. 35.Is 23935 divisible by 8?
  36. 36.Is 4887 divisible by 9?
  37. 37.Is 16154 divisible by 11?
  38. 38.Is 1381 divisible by 7?
  39. 39.Is 4359 divisible by 3?
  40. 40.Is 128801 divisible by 19?

Answer key

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

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