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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 321 · 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 54777 divisible by 15?
  2. 2.Is 62479 divisible by 17?
  3. 3.Is 23658 divisible by 9?
  4. 4.Is 30820 divisible by 30?
  5. 5.Is 7076 divisible by 6?
  6. 6.Is 128720 divisible by 20?
  7. 7.Is 1789 divisible by 5?
  8. 8.Is 144130 divisible by 29?
  9. 9.Is 195056 divisible by 30?
  10. 10.Is 25808 divisible by 10?
  11. 11.Is 11112 divisible by 2?
  12. 12.Is 20715 divisible by 3?
  13. 13.Is 30536 divisible by 8?
  14. 14.Is 34008 divisible by 6?
  15. 15.Is 3788 divisible by 4?
  16. 16.Is 15753 divisible by 8?
  17. 17.Is 49170 divisible by 30?
  18. 18.Is 68688 divisible by 18?
  19. 19.Is 157090 divisible by 23?
  20. 20.Is 82363 divisible by 15?
  21. 21.Is 20523 divisible by 30?
  22. 22.Is 23968 divisible by 4?
  23. 23.Is 129697 divisible by 23?
  24. 24.Is 13200 divisible by 5?
  25. 25.Is 31564 divisible by 13?
  26. 26.Is 40041 divisible by 9?
  27. 27.Is 182497 divisible by 29?
  28. 28.Is 2337 divisible by 19?
  29. 29.Is 26052 divisible by 20?
  30. 30.Is 32166 divisible by 18?
  31. 31.Is 15708 divisible by 6?
  32. 32.Is 65914 divisible by 13?
  33. 33.Is 53592 divisible by 8?
  34. 34.Is 70080 divisible by 24?
  35. 35.Is 20909 divisible by 29?
  36. 36.Is 52896 divisible by 13?
  37. 37.Is 24855 divisible by 9?
  38. 38.Is 27013 divisible by 23?
  39. 39.Is 81900 divisible by 12?
  40. 40.Is 19690 divisible by 6?

Answer key

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

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