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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 690 · 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 38300 divisible by 18?
  2. 2.Is 49225 divisible by 11?
  3. 3.Is 92 divisible by 5?
  4. 4.Is 4133 divisible by 2?
  5. 5.Is 28632 divisible by 12?
  6. 6.Is 12083 divisible by 2?
  7. 7.Is 108739 divisible by 23?
  8. 8.Is 39032 divisible by 7?
  9. 9.Is 15689 divisible by 17?
  10. 10.Is 78758 divisible by 30?
  11. 11.Is 104655 divisible by 15?
  12. 12.Is 40180 divisible by 7?
  13. 13.Is 144210 divisible by 30?
  14. 14.Is 22848 divisible by 17?
  15. 15.Is 29337 divisible by 5?
  16. 16.Is 29813 divisible by 7?
  17. 17.Is 21905 divisible by 20?
  18. 18.Is 3166 divisible by 6?
  19. 19.Is 2946 divisible by 6?
  20. 20.Is 61830 divisible by 9?
  21. 21.Is 30149 divisible by 8?
  22. 22.Is 15396 divisible by 4?
  23. 23.Is 10670 divisible by 13?
  24. 24.Is 65381 divisible by 23?
  25. 25.Is 1497 divisible by 17?
  26. 26.Is 48545 divisible by 7?
  27. 27.Is 16781 divisible by 5?
  28. 28.Is 9315 divisible by 9?
  29. 29.Is 47950 divisible by 10?
  30. 30.Is 84436 divisible by 19?
  31. 31.Is 9595 divisible by 7?
  32. 32.Is 14012 divisible by 4?
  33. 33.Is 17892 divisible by 6?
  34. 34.Is 22840 divisible by 10?
  35. 35.Is 5661 divisible by 23?
  36. 36.Is 168595 divisible by 30?
  37. 37.Is 17475 divisible by 6?
  38. 38.Is 26754 divisible by 19?
  39. 39.Is 62260 divisible by 10?
  40. 40.Is 60994 divisible by 11?

Answer key

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

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