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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 914 · 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 40797 divisible by 9?
  2. 2.Is 15712 divisible by 12?
  3. 3.Is 175890 divisible by 30?
  4. 4.Is 30601 divisible by 9?
  5. 5.Is 74118 divisible by 11?
  6. 6.Is 6641 divisible by 3?
  7. 7.Is 73776 divisible by 29?
  8. 8.Is 36167 divisible by 8?
  9. 9.Is 28204 divisible by 7?
  10. 10.Is 25154 divisible by 18?
  11. 11.Is 110653 divisible by 17?
  12. 12.Is 55490 divisible by 10?
  13. 13.Is 13917 divisible by 3?
  14. 14.Is 5673 divisible by 17?
  15. 15.Is 21819 divisible by 7?
  16. 16.Is 8270 divisible by 5?
  17. 17.Is 12221 divisible by 4?
  18. 18.Is 52499 divisible by 8?
  19. 19.Is 6338 divisible by 4?
  20. 20.Is 88373 divisible by 13?
  21. 21.Is 39936 divisible by 10?
  22. 22.Is 101770 divisible by 18?
  23. 23.Is 7942 divisible by 13?
  24. 24.Is 10320 divisible by 7?
  25. 25.Is 6454 divisible by 2?
  26. 26.Is 19132 divisible by 13?
  27. 27.Is 94095 divisible by 15?
  28. 28.Is 36027 divisible by 8?
  29. 29.Is 158920 divisible by 29?
  30. 30.Is 88689 divisible by 17?
  31. 31.Is 2880 divisible by 2?
  32. 32.Is 7667 divisible by 6?
  33. 33.Is 45081 divisible by 15?
  34. 34.Is 42990 divisible by 15?
  35. 35.Is 79410 divisible by 30?
  36. 36.Is 103785 divisible by 15?
  37. 37.Is 64638 divisible by 18?
  38. 38.Is 21450 divisible by 23?
  39. 39.Is 136574 divisible by 23?
  40. 40.Is 4401 divisible by 9?

Answer key

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

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