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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 933 · 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 91566 divisible by 18?
  2. 2.Is 72456 divisible by 11?
  3. 3.Is 86617 divisible by 18?
  4. 4.Is 45544 divisible by 8?
  5. 5.Is 144384 divisible by 24?
  6. 6.Is 38910 divisible by 30?
  7. 7.Is 19938 divisible by 11?
  8. 8.Is 138360 divisible by 20?
  9. 9.Is 69174 divisible by 18?
  10. 10.Is 58239 divisible by 9?
  11. 11.Is 39559 divisible by 13?
  12. 12.Is 65671 divisible by 17?
  13. 13.Is 40233 divisible by 8?
  14. 14.Is 81013 divisible by 24?
  15. 15.Is 55897 divisible by 12?
  16. 16.Is 10214 divisible by 2?
  17. 17.Is 10586 divisible by 2?
  18. 18.Is 80907 divisible by 30?
  19. 19.Is 3737 divisible by 5?
  20. 20.Is 61277 divisible by 29?
  21. 21.Is 4798 divisible by 3?
  22. 22.Is 7608 divisible by 4?
  23. 23.Is 13964 divisible by 4?
  24. 24.Is 37283 divisible by 23?
  25. 25.Is 2363 divisible by 17?
  26. 26.Is 46935 divisible by 9?
  27. 27.Is 45612 divisible by 12?
  28. 28.Is 30919 divisible by 6?
  29. 29.Is 119832 divisible by 24?
  30. 30.Is 6082 divisible by 3?
  31. 31.Is 123228 divisible by 24?
  32. 32.Is 56856 divisible by 23?
  33. 33.Is 4355 divisible by 13?
  34. 34.Is 8882 divisible by 2?
  35. 35.Is 19743 divisible by 3?
  36. 36.Is 88470 divisible by 15?
  37. 37.Is 6696 divisible by 7?
  38. 38.Is 120216 divisible by 24?
  39. 39.Is 88410 divisible by 15?
  40. 40.Is 65574 divisible by 10?

Answer key

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

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