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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 610 · 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 86502 divisible by 17?
  2. 2.Is 3899 divisible by 2?
  3. 3.Is 910 divisible by 2?
  4. 4.Is 6046 divisible by 4?
  5. 5.Is 4085 divisible by 5?
  6. 6.Is 86810 divisible by 24?
  7. 7.Is 154146 divisible by 23?
  8. 8.Is 142509 divisible by 24?
  9. 9.Is 11160 divisible by 20?
  10. 10.Is 10459 divisible by 5?
  11. 11.Is 2748 divisible by 4?
  12. 12.Is 20057 divisible by 5?
  13. 13.Is 33991 divisible by 19?
  14. 14.Is 78012 divisible by 12?
  15. 15.Is 69480 divisible by 10?
  16. 16.Is 23173 divisible by 6?
  17. 17.Is 136944 divisible by 24?
  18. 18.Is 2368 divisible by 4?
  19. 19.Is 68931 divisible by 12?
  20. 20.Is 21354 divisible by 9?
  21. 21.Is 42377 divisible by 7?
  22. 22.Is 28244 divisible by 23?
  23. 23.Is 32202 divisible by 5?
  24. 24.Is 6244 divisible by 4?
  25. 25.Is 30975 divisible by 13?
  26. 26.Is 104907 divisible by 17?
  27. 27.Is 47553 divisible by 11?
  28. 28.Is 193543 divisible by 29?
  29. 29.Is 96753 divisible by 17?
  30. 30.Is 14465 divisible by 5?
  31. 31.Is 12903 divisible by 11?
  32. 32.Is 68970 divisible by 19?
  33. 33.Is 10572 divisible by 2?
  34. 34.Is 5041 divisible by 4?
  35. 35.Is 20121 divisible by 19?
  36. 36.Is 660 divisible by 4?
  37. 37.Is 20190 divisible by 30?
  38. 38.Is 53240 divisible by 17?
  39. 39.Is 113883 divisible by 18?
  40. 40.Is 37316 divisible by 18?

Answer key

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

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