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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 477 · 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 86764 divisible by 18?
  2. 2.Is 7073 divisible by 2?
  3. 3.Is 33315 divisible by 15?
  4. 4.Is 6846 divisible by 6?
  5. 5.Is 41767 divisible by 29?
  6. 6.Is 101664 divisible by 18?
  7. 7.Is 81224 divisible by 13?
  8. 8.Is 56668 divisible by 23?
  9. 9.Is 50505 divisible by 18?
  10. 10.Is 132031 divisible by 19?
  11. 11.Is 27648 divisible by 8?
  12. 12.Is 33430 divisible by 5?
  13. 13.Is 112631 divisible by 23?
  14. 14.Is 1958 divisible by 11?
  15. 15.Is 40104 divisible by 12?
  16. 16.Is 33408 divisible by 9?
  17. 17.Is 55926 divisible by 9?
  18. 18.Is 117233 divisible by 30?
  19. 19.Is 34146 divisible by 9?
  20. 20.Is 36378 divisible by 18?
  21. 21.Is 16702 divisible by 7?
  22. 22.Is 65663 divisible by 13?
  23. 23.Is 171270 divisible by 30?
  24. 24.Is 5621 divisible by 11?
  25. 25.Is 75379 divisible by 30?
  26. 26.Is 8892 divisible by 2?
  27. 27.Is 43380 divisible by 8?
  28. 28.Is 21576 divisible by 24?
  29. 29.Is 89167 divisible by 19?
  30. 30.Is 10891 divisible by 19?
  31. 31.Is 52632 divisible by 17?
  32. 32.Is 44770 divisible by 13?
  33. 33.Is 44889 divisible by 13?
  34. 34.Is 22290 divisible by 6?
  35. 35.Is 31968 divisible by 18?
  36. 36.Is 118120 divisible by 20?
  37. 37.Is 98940 divisible by 20?
  38. 38.Is 33238 divisible by 9?
  39. 39.Is 1693 divisible by 20?
  40. 40.Is 191628 divisible by 30?

Answer key

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

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