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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 648 · 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 28134 divisible by 9?
  2. 2.Is 18792 divisible by 5?
  3. 3.Is 10590 divisible by 15?
  4. 4.Is 10812 divisible by 4?
  5. 5.Is 13100 divisible by 20?
  6. 6.Is 2479 divisible by 3?
  7. 7.Is 20233 divisible by 15?
  8. 8.Is 59938 divisible by 19?
  9. 9.Is 40490 divisible by 6?
  10. 10.Is 20461 divisible by 3?
  11. 11.Is 95580 divisible by 20?
  12. 12.Is 49119 divisible by 17?
  13. 13.Is 31130 divisible by 17?
  14. 14.Is 3157 divisible by 7?
  15. 15.Is 14191 divisible by 23?
  16. 16.Is 88559 divisible by 24?
  17. 17.Is 7532 divisible by 6?
  18. 18.Is 27810 divisible by 30?
  19. 19.Is 783 divisible by 2?
  20. 20.Is 78190 divisible by 19?
  21. 21.Is 48670 divisible by 7?
  22. 22.Is 149937 divisible by 23?
  23. 23.Is 62950 divisible by 19?
  24. 24.Is 76275 divisible by 15?
  25. 25.Is 7868 divisible by 8?
  26. 26.Is 58728 divisible by 9?
  27. 27.Is 16112 divisible by 4?
  28. 28.Is 45366 divisible by 18?
  29. 29.Is 26134 divisible by 11?
  30. 30.Is 19563 divisible by 9?
  31. 31.Is 44478 divisible by 20?
  32. 32.Is 137494 divisible by 23?
  33. 33.Is 27155 divisible by 4?
  34. 34.Is 7614 divisible by 9?
  35. 35.Is 137628 divisible by 30?
  36. 36.Is 13179 divisible by 2?
  37. 37.Is 47820 divisible by 7?
  38. 38.Is 9092 divisible by 5?
  39. 39.Is 166948 divisible by 29?
  40. 40.Is 15015 divisible by 11?

Answer key

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

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