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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 187 · 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 110126 divisible by 17?
  2. 2.Is 69240 divisible by 30?
  3. 3.Is 1896 divisible by 10?
  4. 4.Is 23283 divisible by 6?
  5. 5.Is 144360 divisible by 30?
  6. 6.Is 18722 divisible by 3?
  7. 7.Is 21640 divisible by 4?
  8. 8.Is 47502 divisible by 13?
  9. 9.Is 19551 divisible by 3?
  10. 10.Is 48889 divisible by 8?
  11. 11.Is 25368 divisible by 7?
  12. 12.Is 39905 divisible by 7?
  13. 13.Is 48440 divisible by 7?
  14. 14.Is 7035 divisible by 7?
  15. 15.Is 92412 divisible by 19?
  16. 16.Is 88766 divisible by 13?
  17. 17.Is 87226 divisible by 29?
  18. 18.Is 100707 divisible by 18?
  19. 19.Is 60269 divisible by 29?
  20. 20.Is 25925 divisible by 5?
  21. 21.Is 21281 divisible by 7?
  22. 22.Is 7286 divisible by 20?
  23. 23.Is 64503 divisible by 11?
  24. 24.Is 10636 divisible by 13?
  25. 25.Is 17688 divisible by 4?
  26. 26.Is 136045 divisible by 23?
  27. 27.Is 38620 divisible by 19?
  28. 28.Is 92483 divisible by 30?
  29. 29.Is 50373 divisible by 9?
  30. 30.Is 39273 divisible by 19?
  31. 31.Is 38449 divisible by 7?
  32. 32.Is 45633 divisible by 11?
  33. 33.Is 11233 divisible by 6?
  34. 34.Is 83772 divisible by 12?
  35. 35.Is 55678 divisible by 10?
  36. 36.Is 112632 divisible by 30?
  37. 37.Is 9666 divisible by 9?
  38. 38.Is 624 divisible by 3?
  39. 39.Is 40194 divisible by 12?
  40. 40.Is 125712 divisible by 18?

Answer key

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

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