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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 345 · 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 30258 divisible by 8?
  2. 2.Is 21680 divisible by 5?
  3. 3.Is 157665 divisible by 23?
  4. 4.Is 22369 divisible by 4?
  5. 5.Is 144377 divisible by 29?
  6. 6.Is 90090 divisible by 15?
  7. 7.Is 125016 divisible by 24?
  8. 8.Is 39420 divisible by 9?
  9. 9.Is 48223 divisible by 8?
  10. 10.Is 83214 divisible by 18?
  11. 11.Is 20080 divisible by 4?
  12. 12.Is 80948 divisible by 19?
  13. 13.Is 110234 divisible by 29?
  14. 14.Is 36312 divisible by 8?
  15. 15.Is 55601 divisible by 11?
  16. 16.Is 1741 divisible by 2?
  17. 17.Is 65717 divisible by 12?
  18. 18.Is 35868 divisible by 6?
  19. 19.Is 89791 divisible by 15?
  20. 20.Is 2386 divisible by 3?
  21. 21.Is 113297 divisible by 18?
  22. 22.Is 71688 divisible by 24?
  23. 23.Is 40194 divisible by 6?
  24. 24.Is 9191 divisible by 7?
  25. 25.Is 7548 divisible by 4?
  26. 26.Is 88098 divisible by 13?
  27. 27.Is 4200 divisible by 6?
  28. 28.Is 13725 divisible by 2?
  29. 29.Is 12180 divisible by 6?
  30. 30.Is 119797 divisible by 19?
  31. 31.Is 34401 divisible by 24?
  32. 32.Is 104025 divisible by 20?
  33. 33.Is 91798 divisible by 19?
  34. 34.Is 137880 divisible by 20?
  35. 35.Is 35283 divisible by 18?
  36. 36.Is 69295 divisible by 19?
  37. 37.Is 203602 divisible by 30?
  38. 38.Is 6357 divisible by 6?
  39. 39.Is 34481 divisible by 29?
  40. 40.Is 74152 divisible by 23?

Answer key

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

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