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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 899 · 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 18294 divisible by 3?
  2. 2.Is 4654 divisible by 13?
  3. 3.Is 94770 divisible by 15?
  4. 4.Is 114683 divisible by 18?
  5. 5.Is 10538 divisible by 6?
  6. 6.Is 21698 divisible by 19?
  7. 7.Is 61946 divisible by 19?
  8. 8.Is 106053 divisible by 29?
  9. 9.Is 19152 divisible by 19?
  10. 10.Is 7215 divisible by 13?
  11. 11.Is 6793 divisible by 2?
  12. 12.Is 13140 divisible by 30?
  13. 13.Is 53520 divisible by 9?
  14. 14.Is 14971 divisible by 5?
  15. 15.Is 40404 divisible by 12?
  16. 16.Is 19418 divisible by 17?
  17. 17.Is 1449 divisible by 5?
  18. 18.Is 32599 divisible by 10?
  19. 19.Is 72011 divisible by 17?
  20. 20.Is 73531 divisible by 17?
  21. 21.Is 31895 divisible by 19?
  22. 22.Is 9305 divisible by 5?
  23. 23.Is 56189 divisible by 9?
  24. 24.Is 49520 divisible by 20?
  25. 25.Is 17691 divisible by 7?
  26. 26.Is 22860 divisible by 6?
  27. 27.Is 32708 divisible by 17?
  28. 28.Is 87 divisible by 2?
  29. 29.Is 38759 divisible by 20?
  30. 30.Is 9224 divisible by 2?
  31. 31.Is 4926 divisible by 18?
  32. 32.Is 78477 divisible by 13?
  33. 33.Is 58304 divisible by 9?
  34. 34.Is 30595 divisible by 29?
  35. 35.Is 15426 divisible by 8?
  36. 36.Is 161208 divisible by 24?
  37. 37.Is 41258 divisible by 7?
  38. 38.Is 74460 divisible by 30?
  39. 39.Is 85248 divisible by 18?
  40. 40.Is 76997 divisible by 30?

Answer key

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

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