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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 571 · 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 39382 divisible by 29?
  2. 2.Is 13163 divisible by 10?
  3. 3.Is 6206 divisible by 12?
  4. 4.Is 7118 divisible by 4?
  5. 5.Is 6280 divisible by 2?
  6. 6.Is 70743 divisible by 24?
  7. 7.Is 35663 divisible by 19?
  8. 8.Is 75525 divisible by 15?
  9. 9.Is 35235 divisible by 15?
  10. 10.Is 16365 divisible by 5?
  11. 11.Is 70830 divisible by 18?
  12. 12.Is 60544 divisible by 13?
  13. 13.Is 62588 divisible by 10?
  14. 14.Is 92085 divisible by 15?
  15. 15.Is 15640 divisible by 17?
  16. 16.Is 19357 divisible by 13?
  17. 17.Is 68039 divisible by 12?
  18. 18.Is 106376 divisible by 23?
  19. 19.Is 6310 divisible by 2?
  20. 20.Is 20940 divisible by 30?
  21. 21.Is 84170 divisible by 19?
  22. 22.Is 10354 divisible by 8?
  23. 23.Is 37476 divisible by 18?
  24. 24.Is 32031 divisible by 10?
  25. 25.Is 14220 divisible by 18?
  26. 26.Is 84262 divisible by 23?
  27. 27.Is 21171 divisible by 20?
  28. 28.Is 14990 divisible by 9?
  29. 29.Is 46836 divisible by 9?
  30. 30.Is 24149 divisible by 6?
  31. 31.Is 37241 divisible by 17?
  32. 32.Is 78537 divisible by 15?
  33. 33.Is 4715 divisible by 23?
  34. 34.Is 20688 divisible by 3?
  35. 35.Is 58006 divisible by 13?
  36. 36.Is 51150 divisible by 9?
  37. 37.Is 19284 divisible by 12?
  38. 38.Is 62073 divisible by 9?
  39. 39.Is 4252 divisible by 2?
  40. 40.Is 54213 divisible by 17?

Answer key

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

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