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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 965 · 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 155753 divisible by 29?
  2. 2.Is 6480 divisible by 24?
  3. 3.Is 46342 divisible by 23?
  4. 4.Is 8948 divisible by 11?
  5. 5.Is 15420 divisible by 5?
  6. 6.Is 14296 divisible by 7?
  7. 7.Is 13187 divisible by 11?
  8. 8.Is 16874 divisible by 3?
  9. 9.Is 28210 divisible by 6?
  10. 10.Is 94815 divisible by 15?
  11. 11.Is 101264 divisible by 17?
  12. 12.Is 516 divisible by 12?
  13. 13.Is 20192 divisible by 4?
  14. 14.Is 11142 divisible by 18?
  15. 15.Is 198 divisible by 9?
  16. 16.Is 46750 divisible by 7?
  17. 17.Is 132030 divisible by 30?
  18. 18.Is 48603 divisible by 17?
  19. 19.Is 153178 divisible by 29?
  20. 20.Is 41340 divisible by 24?
  21. 21.Is 70863 divisible by 13?
  22. 22.Is 27750 divisible by 5?
  23. 23.Is 183431 divisible by 30?
  24. 24.Is 10250 divisible by 5?
  25. 25.Is 14970 divisible by 11?
  26. 26.Is 123209 divisible by 18?
  27. 27.Is 9196 divisible by 5?
  28. 28.Is 75614 divisible by 12?
  29. 29.Is 40824 divisible by 18?
  30. 30.Is 8088 divisible by 4?
  31. 31.Is 3887 divisible by 3?
  32. 32.Is 5760 divisible by 6?
  33. 33.Is 49764 divisible by 29?
  34. 34.Is 2290 divisible by 5?
  35. 35.Is 11905 divisible by 11?
  36. 36.Is 44120 divisible by 13?
  37. 37.Is 10406 divisible by 8?
  38. 38.Is 20505 divisible by 5?
  39. 39.Is 14706 divisible by 18?
  40. 40.Is 5865 divisible by 18?

Answer key

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

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