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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 762 · 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 118845 divisible by 19?
  2. 2.Is 1878 divisible by 2?
  3. 3.Is 122407 divisible by 30?
  4. 4.Is 58423 divisible by 11?
  5. 5.Is 47056 divisible by 7?
  6. 6.Is 33828 divisible by 12?
  7. 7.Is 5754 divisible by 2?
  8. 8.Is 65704 divisible by 19?
  9. 9.Is 29006 divisible by 7?
  10. 10.Is 45948 divisible by 23?
  11. 11.Is 101942 divisible by 20?
  12. 12.Is 26152 divisible by 8?
  13. 13.Is 45419 divisible by 11?
  14. 14.Is 56615 divisible by 20?
  15. 15.Is 22855 divisible by 8?
  16. 16.Is 27380 divisible by 20?
  17. 17.Is 72930 divisible by 11?
  18. 18.Is 16423 divisible by 3?
  19. 19.Is 5776 divisible by 6?
  20. 20.Is 73094 divisible by 23?
  21. 21.Is 43452 divisible by 9?
  22. 22.Is 26478 divisible by 18?
  23. 23.Is 58235 divisible by 10?
  24. 24.Is 10020 divisible by 30?
  25. 25.Is 5229 divisible by 3?
  26. 26.Is 108328 divisible by 18?
  27. 27.Is 42934 divisible by 19?
  28. 28.Is 34160 divisible by 10?
  29. 29.Is 84 divisible by 2?
  30. 30.Is 29141 divisible by 8?
  31. 31.Is 51281 divisible by 11?
  32. 32.Is 12537 divisible by 20?
  33. 33.Is 14208 divisible by 11?
  34. 34.Is 46532 divisible by 9?
  35. 35.Is 61745 divisible by 12?
  36. 36.Is 602 divisible by 13?
  37. 37.Is 48905 divisible by 10?
  38. 38.Is 12327 divisible by 10?
  39. 39.Is 70381 divisible by 20?
  40. 40.Is 22242 divisible by 11?

Answer key

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

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