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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 846 · 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 30571 divisible by 19?
  2. 2.Is 27815 divisible by 5?
  3. 3.Is 29196 divisible by 12?
  4. 4.Is 65502 divisible by 18?
  5. 5.Is 88185 divisible by 15?
  6. 6.Is 31983 divisible by 7?
  7. 7.Is 45522 divisible by 18?
  8. 8.Is 22134 divisible by 7?
  9. 9.Is 65048 divisible by 23?
  10. 10.Is 29088 divisible by 18?
  11. 11.Is 60270 divisible by 10?
  12. 12.Is 8163 divisible by 5?
  13. 13.Is 7744 divisible by 3?
  14. 14.Is 105532 divisible by 19?
  15. 15.Is 7257 divisible by 5?
  16. 16.Is 73905 divisible by 13?
  17. 17.Is 76470 divisible by 15?
  18. 18.Is 5260 divisible by 4?
  19. 19.Is 85504 divisible by 17?
  20. 20.Is 11947 divisible by 13?
  21. 21.Is 33897 divisible by 12?
  22. 22.Is 28354 divisible by 11?
  23. 23.Is 15192 divisible by 8?
  24. 24.Is 97484 divisible by 15?
  25. 25.Is 17132 divisible by 7?
  26. 26.Is 90084 divisible by 20?
  27. 27.Is 6199 divisible by 5?
  28. 28.Is 24582 divisible by 15?
  29. 29.Is 13364 divisible by 10?
  30. 30.Is 44807 divisible by 23?
  31. 31.Is 71926 divisible by 12?
  32. 32.Is 80664 divisible by 12?
  33. 33.Is 33260 divisible by 10?
  34. 34.Is 35780 divisible by 20?
  35. 35.Is 98484 divisible by 29?
  36. 36.Is 39624 divisible by 12?
  37. 37.Is 70434 divisible by 18?
  38. 38.Is 76287 divisible by 11?
  39. 39.Is 65307 divisible by 11?
  40. 40.Is 104970 divisible by 30?

Answer key

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

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