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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 507 · 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 30715 divisible by 8?
  2. 2.Is 99288 divisible by 19?
  3. 3.Is 24024 divisible by 8?
  4. 4.Is 85898 divisible by 29?
  5. 5.Is 5833 divisible by 18?
  6. 6.Is 135768 divisible by 20?
  7. 7.Is 1911 divisible by 7?
  8. 8.Is 15276 divisible by 4?
  9. 9.Is 198559 divisible by 30?
  10. 10.Is 6000 divisible by 6?
  11. 11.Is 10942 divisible by 5?
  12. 12.Is 3029 divisible by 17?
  13. 13.Is 27440 divisible by 8?
  14. 14.Is 51510 divisible by 11?
  15. 15.Is 10916 divisible by 10?
  16. 16.Is 104113 divisible by 15?
  17. 17.Is 24636 divisible by 6?
  18. 18.Is 60138 divisible by 18?
  19. 19.Is 2940 divisible by 2?
  20. 20.Is 95322 divisible by 17?
  21. 21.Is 109064 divisible by 18?
  22. 22.Is 3919 divisible by 6?
  23. 23.Is 9234 divisible by 6?
  24. 24.Is 19370 divisible by 5?
  25. 25.Is 10337 divisible by 15?
  26. 26.Is 13353 divisible by 2?
  27. 27.Is 64528 divisible by 15?
  28. 28.Is 121344 divisible by 20?
  29. 29.Is 406 divisible by 5?
  30. 30.Is 60044 divisible by 17?
  31. 31.Is 41481 divisible by 11?
  32. 32.Is 21956 divisible by 5?
  33. 33.Is 71024 divisible by 19?
  34. 34.Is 13740 divisible by 6?
  35. 35.Is 28521 divisible by 9?
  36. 36.Is 30671 divisible by 9?
  37. 37.Is 24639 divisible by 23?
  38. 38.Is 50296 divisible by 11?
  39. 39.Is 29757 divisible by 13?
  40. 40.Is 32944 divisible by 29?

Answer key

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

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