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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 355 · 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 1710 divisible by 6?
  2. 2.Is 43849 divisible by 9?
  3. 3.Is 40188 divisible by 6?
  4. 4.Is 9980 divisible by 5?
  5. 5.Is 7408 divisible by 4?
  6. 6.Is 21329 divisible by 18?
  7. 7.Is 138647 divisible by 23?
  8. 8.Is 98022 divisible by 17?
  9. 9.Is 21961 divisible by 5?
  10. 10.Is 34808 divisible by 12?
  11. 11.Is 152960 divisible by 23?
  12. 12.Is 5829 divisible by 7?
  13. 13.Is 16860 divisible by 15?
  14. 14.Is 40811 divisible by 6?
  15. 15.Is 1888 divisible by 4?
  16. 16.Is 128527 divisible by 30?
  17. 17.Is 162373 divisible by 24?
  18. 18.Is 30693 divisible by 6?
  19. 19.Is 44755 divisible by 19?
  20. 20.Is 146855 divisible by 23?
  21. 21.Is 38570 divisible by 19?
  22. 22.Is 28799 divisible by 7?
  23. 23.Is 123081 divisible by 20?
  24. 24.Is 20345 divisible by 3?
  25. 25.Is 25350 divisible by 7?
  26. 26.Is 55839 divisible by 19?
  27. 27.Is 11372 divisible by 8?
  28. 28.Is 8850 divisible by 15?
  29. 29.Is 15072 divisible by 4?
  30. 30.Is 12522 divisible by 3?
  31. 31.Is 5318 divisible by 15?
  32. 32.Is 44993 divisible by 17?
  33. 33.Is 65280 divisible by 11?
  34. 34.Is 59613 divisible by 9?
  35. 35.Is 65351 divisible by 13?
  36. 36.Is 37344 divisible by 12?
  37. 37.Is 8742 divisible by 3?
  38. 38.Is 1143 divisible by 10?
  39. 39.Is 62878 divisible by 20?
  40. 40.Is 29848 divisible by 8?

Answer key

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

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