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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 619 · 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 122904 divisible by 24?
  2. 2.Is 131152 divisible by 23?
  3. 3.Is 27667 divisible by 10?
  4. 4.Is 176469 divisible by 29?
  5. 5.Is 25283 divisible by 23?
  6. 6.Is 14688 divisible by 10?
  7. 7.Is 48677 divisible by 17?
  8. 8.Is 24308 divisible by 4?
  9. 9.Is 25104 divisible by 20?
  10. 10.Is 36958 divisible by 24?
  11. 11.Is 12687 divisible by 5?
  12. 12.Is 79317 divisible by 20?
  13. 13.Is 16905 divisible by 3?
  14. 14.Is 196309 divisible by 30?
  15. 15.Is 75844 divisible by 12?
  16. 16.Is 29522 divisible by 29?
  17. 17.Is 14040 divisible by 5?
  18. 18.Is 38697 divisible by 11?
  19. 19.Is 23212 divisible by 4?
  20. 20.Is 22356 divisible by 23?
  21. 21.Is 64260 divisible by 13?
  22. 22.Is 78972 divisible by 24?
  23. 23.Is 107987 divisible by 30?
  24. 24.Is 84476 divisible by 15?
  25. 25.Is 78769 divisible by 30?
  26. 26.Is 88478 divisible by 13?
  27. 27.Is 14636 divisible by 4?
  28. 28.Is 445 divisible by 5?
  29. 29.Is 185896 divisible by 30?
  30. 30.Is 54584 divisible by 10?
  31. 31.Is 41059 divisible by 19?
  32. 32.Is 3392 divisible by 2?
  33. 33.Is 78545 divisible by 30?
  34. 34.Is 94831 divisible by 29?
  35. 35.Is 11911 divisible by 6?
  36. 36.Is 7281 divisible by 20?
  37. 37.Is 28100 divisible by 10?
  38. 38.Is 1164 divisible by 6?
  39. 39.Is 158662 divisible by 23?
  40. 40.Is 15154 divisible by 29?

Answer key

  1. yes
  2. no
  3. no
  4. no
  5. no
  6. no
  7. no
  8. yes
  9. no
  10. no
  11. no
  12. no
  13. yes
  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. yes
  27. yes
  28. yes
  29. no
  30. no
  31. yes
  32. yes
  33. no
  34. no
  35. no
  36. no
  37. yes
  38. yes
  39. no
  40. no

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