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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 623 · 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 32877 divisible by 9?
  2. 2.Is 11107 divisible by 29?
  3. 3.Is 7134 divisible by 4?
  4. 4.Is 39712 divisible by 8?
  5. 5.Is 4950 divisible by 15?
  6. 6.Is 86665 divisible by 23?
  7. 7.Is 10152 divisible by 4?
  8. 8.Is 393 divisible by 15?
  9. 9.Is 29337 divisible by 11?
  10. 10.Is 53463 divisible by 8?
  11. 11.Is 52940 divisible by 18?
  12. 12.Is 35568 divisible by 19?
  13. 13.Is 9740 divisible by 20?
  14. 14.Is 16376 divisible by 9?
  15. 15.Is 96655 divisible by 19?
  16. 16.Is 33444 divisible by 13?
  17. 17.Is 41243 divisible by 17?
  18. 18.Is 27172 divisible by 11?
  19. 19.Is 43627 divisible by 20?
  20. 20.Is 71729 divisible by 18?
  21. 21.Is 5742 divisible by 6?
  22. 22.Is 34342 divisible by 13?
  23. 23.Is 32253 divisible by 7?
  24. 24.Is 18894 divisible by 3?
  25. 25.Is 22241 divisible by 12?
  26. 26.Is 43860 divisible by 30?
  27. 27.Is 3622 divisible by 3?
  28. 28.Is 72120 divisible by 30?
  29. 29.Is 169948 divisible by 30?
  30. 30.Is 16717 divisible by 10?
  31. 31.Is 7513 divisible by 8?
  32. 32.Is 30318 divisible by 23?
  33. 33.Is 19176 divisible by 7?
  34. 34.Is 32419 divisible by 17?
  35. 35.Is 40706 divisible by 6?
  36. 36.Is 27814 divisible by 4?
  37. 37.Is 2852 divisible by 4?
  38. 38.Is 37129 divisible by 6?
  39. 39.Is 3072 divisible by 6?
  40. 40.Is 21270 divisible by 10?

Answer key

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

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