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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 282 · 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 74819 divisible by 23?
  2. 2.Is 56570 divisible by 17?
  3. 3.Is 25568 divisible by 18?
  4. 4.Is 13344 divisible by 12?
  5. 5.Is 74696 divisible by 24?
  6. 6.Is 76908 divisible by 13?
  7. 7.Is 12275 divisible by 5?
  8. 8.Is 15527 divisible by 3?
  9. 9.Is 150865 divisible by 23?
  10. 10.Is 110515 divisible by 23?
  11. 11.Is 7336 divisible by 8?
  12. 12.Is 53705 divisible by 23?
  13. 13.Is 40622 divisible by 19?
  14. 14.Is 22790 divisible by 9?
  15. 15.Is 87228 divisible by 29?
  16. 16.Is 32699 divisible by 18?
  17. 17.Is 6260 divisible by 2?
  18. 18.Is 26021 divisible by 18?
  19. 19.Is 69839 divisible by 11?
  20. 20.Is 72103 divisible by 11?
  21. 21.Is 2867 divisible by 11?
  22. 22.Is 52845 divisible by 15?
  23. 23.Is 74129 divisible by 15?
  24. 24.Is 111473 divisible by 19?
  25. 25.Is 27713 divisible by 9?
  26. 26.Is 12201 divisible by 7?
  27. 27.Is 25529 divisible by 5?
  28. 28.Is 121961 divisible by 19?
  29. 29.Is 62077 divisible by 23?
  30. 30.Is 38025 divisible by 9?
  31. 31.Is 45630 divisible by 15?
  32. 32.Is 95809 divisible by 15?
  33. 33.Is 689 divisible by 17?
  34. 34.Is 2724 divisible by 23?
  35. 35.Is 1496 divisible by 3?
  36. 36.Is 10458 divisible by 9?
  37. 37.Is 60201 divisible by 9?
  38. 38.Is 7620 divisible by 20?
  39. 39.Is 26841 divisible by 10?
  40. 40.Is 50601 divisible by 13?

Answer key

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

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