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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 721 · 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 116616 divisible by 24?
  2. 2.Is 109784 divisible by 19?
  3. 3.Is 41650 divisible by 17?
  4. 4.Is 41384 divisible by 8?
  5. 5.Is 30414 divisible by 6?
  6. 6.Is 104371 divisible by 29?
  7. 7.Is 17136 divisible by 12?
  8. 8.Is 120570 divisible by 30?
  9. 9.Is 14022 divisible by 3?
  10. 10.Is 18892 divisible by 4?
  11. 11.Is 55546 divisible by 17?
  12. 12.Is 8541 divisible by 2?
  13. 13.Is 6676 divisible by 13?
  14. 14.Is 41647 divisible by 17?
  15. 15.Is 49513 divisible by 23?
  16. 16.Is 58190 divisible by 11?
  17. 17.Is 12221 divisible by 11?
  18. 18.Is 33725 divisible by 9?
  19. 19.Is 74436 divisible by 12?
  20. 20.Is 18576 divisible by 9?
  21. 21.Is 6840 divisible by 13?
  22. 22.Is 122516 divisible by 20?
  23. 23.Is 17047 divisible by 23?
  24. 24.Is 19081 divisible by 3?
  25. 25.Is 49960 divisible by 11?
  26. 26.Is 28338 divisible by 17?
  27. 27.Is 9241 divisible by 2?
  28. 28.Is 2232 divisible by 18?
  29. 29.Is 166512 divisible by 24?
  30. 30.Is 114692 divisible by 20?
  31. 31.Is 99603 divisible by 17?
  32. 32.Is 34752 divisible by 24?
  33. 33.Is 5908 divisible by 7?
  34. 34.Is 32427 divisible by 30?
  35. 35.Is 48084 divisible by 18?
  36. 36.Is 16935 divisible by 3?
  37. 37.Is 34170 divisible by 30?
  38. 38.Is 48555 divisible by 9?
  39. 39.Is 33492 divisible by 8?
  40. 40.Is 74290 divisible by 18?

Answer key

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

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