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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 17 · 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 29799 divisible by 6?
  2. 2.Is 18230 divisible by 10?
  3. 3.Is 44576 divisible by 8?
  4. 4.Is 20772 divisible by 6?
  5. 5.Is 4895 divisible by 5?
  6. 6.Is 77016 divisible by 12?
  7. 7.Is 49179 divisible by 13?
  8. 8.Is 17894 divisible by 10?
  9. 9.Is 7219 divisible by 2?
  10. 10.Is 24384 divisible by 17?
  11. 11.Is 44800 divisible by 7?
  12. 12.Is 23424 divisible by 29?
  13. 13.Is 5096 divisible by 6?
  14. 14.Is 33931 divisible by 8?
  15. 15.Is 9671 divisible by 30?
  16. 16.Is 36915 divisible by 15?
  17. 17.Is 29091 divisible by 8?
  18. 18.Is 9233 divisible by 3?
  19. 19.Is 50196 divisible by 12?
  20. 20.Is 1741 divisible by 2?
  21. 21.Is 28712 divisible by 5?
  22. 22.Is 30842 divisible by 5?
  23. 23.Is 8877 divisible by 2?
  24. 24.Is 9860 divisible by 20?
  25. 25.Is 34867 divisible by 7?
  26. 26.Is 42784 divisible by 7?
  27. 27.Is 64069 divisible by 11?
  28. 28.Is 15115 divisible by 6?
  29. 29.Is 40620 divisible by 30?
  30. 30.Is 13674 divisible by 15?
  31. 31.Is 76176 divisible by 23?
  32. 32.Is 49597 divisible by 30?
  33. 33.Is 11140 divisible by 8?
  34. 34.Is 43770 divisible by 11?
  35. 35.Is 13312 divisible by 3?
  36. 36.Is 6741 divisible by 7?
  37. 37.Is 30000 divisible by 6?
  38. 38.Is 14499 divisible by 3?
  39. 39.Is 12800 divisible by 3?
  40. 40.Is 194007 divisible by 29?

Answer key

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

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