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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 221 · 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 22100 divisible by 4?
  2. 2.Is 45940 divisible by 10?
  3. 3.Is 115295 divisible by 19?
  4. 4.Is 8628 divisible by 4?
  5. 5.Is 99818 divisible by 29?
  6. 6.Is 76464 divisible by 12?
  7. 7.Is 11659 divisible by 13?
  8. 8.Is 21510 divisible by 4?
  9. 9.Is 63086 divisible by 19?
  10. 10.Is 24181 divisible by 30?
  11. 11.Is 10332 divisible by 12?
  12. 12.Is 17227 divisible by 5?
  13. 13.Is 6521 divisible by 3?
  14. 14.Is 11621 divisible by 17?
  15. 15.Is 23044 divisible by 4?
  16. 16.Is 3196 divisible by 17?
  17. 17.Is 67424 divisible by 11?
  18. 18.Is 20796 divisible by 12?
  19. 19.Is 2097 divisible by 2?
  20. 20.Is 8079 divisible by 5?
  21. 21.Is 45861 divisible by 7?
  22. 22.Is 4885 divisible by 3?
  23. 23.Is 17733 divisible by 23?
  24. 24.Is 4908 divisible by 6?
  25. 25.Is 90220 divisible by 20?
  26. 26.Is 178205 divisible by 29?
  27. 27.Is 9776 divisible by 4?
  28. 28.Is 3929 divisible by 5?
  29. 29.Is 70239 divisible by 13?
  30. 30.Is 40559 divisible by 13?
  31. 31.Is 22849 divisible by 7?
  32. 32.Is 52469 divisible by 29?
  33. 33.Is 24856 divisible by 8?
  34. 34.Is 3245 divisible by 5?
  35. 35.Is 26662 divisible by 9?
  36. 36.Is 1300 divisible by 4?
  37. 37.Is 26572 divisible by 7?
  38. 38.Is 102442 divisible by 23?
  39. 39.Is 106495 divisible by 24?
  40. 40.Is 1098 divisible by 20?

Answer key

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

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