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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 810 · 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 52508 divisible by 10?
  2. 2.Is 63315 divisible by 11?
  3. 3.Is 188131 divisible by 29?
  4. 4.Is 8410 divisible by 10?
  5. 5.Is 27891 divisible by 5?
  6. 6.Is 119853 divisible by 24?
  7. 7.Is 25350 divisible by 5?
  8. 8.Is 40340 divisible by 23?
  9. 9.Is 53065 divisible by 10?
  10. 10.Is 58260 divisible by 15?
  11. 11.Is 137952 divisible by 24?
  12. 12.Is 54930 divisible by 15?
  13. 13.Is 18648 divisible by 7?
  14. 14.Is 122970 divisible by 30?
  15. 15.Is 23010 divisible by 30?
  16. 16.Is 30380 divisible by 10?
  17. 17.Is 24390 divisible by 29?
  18. 18.Is 7049 divisible by 15?
  19. 19.Is 45339 divisible by 7?
  20. 20.Is 16236 divisible by 5?
  21. 21.Is 75950 divisible by 29?
  22. 22.Is 26605 divisible by 9?
  23. 23.Is 8700 divisible by 20?
  24. 24.Is 12853 divisible by 12?
  25. 25.Is 25799 divisible by 18?
  26. 26.Is 104846 divisible by 18?
  27. 27.Is 40606 divisible by 11?
  28. 28.Is 33074 divisible by 12?
  29. 29.Is 77832 divisible by 18?
  30. 30.Is 21440 divisible by 20?
  31. 31.Is 97632 divisible by 24?
  32. 32.Is 22229 divisible by 9?
  33. 33.Is 64864 divisible by 12?
  34. 34.Is 3904 divisible by 24?
  35. 35.Is 35799 divisible by 8?
  36. 36.Is 8346 divisible by 13?
  37. 37.Is 4812 divisible by 4?
  38. 38.Is 34175 divisible by 20?
  39. 39.Is 87768 divisible by 23?
  40. 40.Is 34199 divisible by 11?

Answer key

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

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