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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 319 · 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 39806 divisible by 13?
  2. 2.Is 42734 divisible by 23?
  3. 3.Is 9936 divisible by 2?
  4. 4.Is 26544 divisible by 12?
  5. 5.Is 12769 divisible by 23?
  6. 6.Is 118836 divisible by 18?
  7. 7.Is 33600 divisible by 30?
  8. 8.Is 3613 divisible by 2?
  9. 9.Is 25811 divisible by 18?
  10. 10.Is 27736 divisible by 5?
  11. 11.Is 20245 divisible by 4?
  12. 12.Is 9929 divisible by 2?
  13. 13.Is 32455 divisible by 11?
  14. 14.Is 25134 divisible by 11?
  15. 15.Is 55830 divisible by 30?
  16. 16.Is 89161 divisible by 19?
  17. 17.Is 107106 divisible by 20?
  18. 18.Is 6735 divisible by 2?
  19. 19.Is 14279 divisible by 3?
  20. 20.Is 71247 divisible by 17?
  21. 21.Is 14310 divisible by 18?
  22. 22.Is 105781 divisible by 20?
  23. 23.Is 103515 divisible by 15?
  24. 24.Is 51272 divisible by 13?
  25. 25.Is 16770 divisible by 3?
  26. 26.Is 38241 divisible by 7?
  27. 27.Is 20542 divisible by 6?
  28. 28.Is 93860 divisible by 15?
  29. 29.Is 120498 divisible by 19?
  30. 30.Is 576 divisible by 4?
  31. 31.Is 4062 divisible by 4?
  32. 32.Is 27320 divisible by 4?
  33. 33.Is 14882 divisible by 7?
  34. 34.Is 15032 divisible by 5?
  35. 35.Is 14910 divisible by 7?
  36. 36.Is 48695 divisible by 8?
  37. 37.Is 44715 divisible by 9?
  38. 38.Is 6775 divisible by 2?
  39. 39.Is 14310 divisible by 6?
  40. 40.Is 43620 divisible by 17?

Answer key

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

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