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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 662 · 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 31549 divisible by 8?
  2. 2.Is 175980 divisible by 30?
  3. 3.Is 8760 divisible by 19?
  4. 4.Is 127311 divisible by 23?
  5. 5.Is 185165 divisible by 29?
  6. 6.Is 69839 divisible by 11?
  7. 7.Is 16250 divisible by 10?
  8. 8.Is 943 divisible by 3?
  9. 9.Is 2212 divisible by 7?
  10. 10.Is 91316 divisible by 15?
  11. 11.Is 42624 divisible by 8?
  12. 12.Is 111435 divisible by 23?
  13. 13.Is 40971 divisible by 12?
  14. 14.Is 19458 divisible by 6?
  15. 15.Is 38109 divisible by 7?
  16. 16.Is 35694 divisible by 9?
  17. 17.Is 48722 divisible by 9?
  18. 18.Is 67283 divisible by 17?
  19. 19.Is 9618 divisible by 9?
  20. 20.Is 7178 divisible by 2?
  21. 21.Is 85772 divisible by 13?
  22. 22.Is 81778 divisible by 15?
  23. 23.Is 20276 divisible by 3?
  24. 24.Is 77395 divisible by 23?
  25. 25.Is 19850 divisible by 18?
  26. 26.Is 11056 divisible by 4?
  27. 27.Is 19207 divisible by 7?
  28. 28.Is 42770 divisible by 7?
  29. 29.Is 18917 divisible by 3?
  30. 30.Is 15451 divisible by 23?
  31. 31.Is 25308 divisible by 12?
  32. 32.Is 40342 divisible by 8?
  33. 33.Is 5904 divisible by 24?
  34. 34.Is 50909 divisible by 9?
  35. 35.Is 59514 divisible by 13?
  36. 36.Is 122724 divisible by 20?
  37. 37.Is 80541 divisible by 19?
  38. 38.Is 15591 divisible by 5?
  39. 39.Is 50787 divisible by 9?
  40. 40.Is 69552 divisible by 24?

Answer key

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

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