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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 34 · 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 58042 divisible by 12?
  2. 2.Is 35973 divisible by 9?
  3. 3.Is 3521 divisible by 9?
  4. 4.Is 11550 divisible by 7?
  5. 5.Is 2038 divisible by 9?
  6. 6.Is 23108 divisible by 4?
  7. 7.Is 10990 divisible by 7?
  8. 8.Is 40178 divisible by 7?
  9. 9.Is 76690 divisible by 20?
  10. 10.Is 1292 divisible by 19?
  11. 11.Is 24962 divisible by 13?
  12. 12.Is 108598 divisible by 19?
  13. 13.Is 132484 divisible by 23?
  14. 14.Is 121285 divisible by 20?
  15. 15.Is 94460 divisible by 20?
  16. 16.Is 23560 divisible by 20?
  17. 17.Is 8315 divisible by 19?
  18. 18.Is 17379 divisible by 4?
  19. 19.Is 9434 divisible by 30?
  20. 20.Is 16238 divisible by 23?
  21. 21.Is 4907 divisible by 7?
  22. 22.Is 122364 divisible by 23?
  23. 23.Is 12711 divisible by 2?
  24. 24.Is 17515 divisible by 4?
  25. 25.Is 11839 divisible by 7?
  26. 26.Is 52489 divisible by 12?
  27. 27.Is 109720 divisible by 20?
  28. 28.Is 5176 divisible by 8?
  29. 29.Is 73167 divisible by 11?
  30. 30.Is 39515 divisible by 24?
  31. 31.Is 11689 divisible by 13?
  32. 32.Is 19575 divisible by 17?
  33. 33.Is 60966 divisible by 17?
  34. 34.Is 32324 divisible by 6?
  35. 35.Is 155150 divisible by 29?
  36. 36.Is 58338 divisible by 9?
  37. 37.Is 38045 divisible by 7?
  38. 38.Is 110570 divisible by 30?
  39. 39.Is 49440 divisible by 11?
  40. 40.Is 103080 divisible by 24?

Answer key

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

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