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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 538 · 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 31830 divisible by 5?
  2. 2.Is 18842 divisible by 15?
  3. 3.Is 39802 divisible by 7?
  4. 4.Is 23786 divisible by 4?
  5. 5.Is 50220 divisible by 10?
  6. 6.Is 53704 divisible by 23?
  7. 7.Is 71424 divisible by 12?
  8. 8.Is 53205 divisible by 15?
  9. 9.Is 70369 divisible by 13?
  10. 10.Is 122940 divisible by 20?
  11. 11.Is 14611 divisible by 5?
  12. 12.Is 10971 divisible by 2?
  13. 13.Is 103990 divisible by 17?
  14. 14.Is 12596 divisible by 5?
  15. 15.Is 23709 divisible by 6?
  16. 16.Is 64605 divisible by 11?
  17. 17.Is 37362 divisible by 13?
  18. 18.Is 27891 divisible by 9?
  19. 19.Is 44207 divisible by 24?
  20. 20.Is 80911 divisible by 23?
  21. 21.Is 7831 divisible by 2?
  22. 22.Is 157665 divisible by 24?
  23. 23.Is 4552 divisible by 7?
  24. 24.Is 4911 divisible by 7?
  25. 25.Is 132580 divisible by 24?
  26. 26.Is 76512 divisible by 24?
  27. 27.Is 14925 divisible by 3?
  28. 28.Is 70109 divisible by 20?
  29. 29.Is 9612 divisible by 7?
  30. 30.Is 21527 divisible by 4?
  31. 31.Is 33479 divisible by 17?
  32. 32.Is 142638 divisible by 24?
  33. 33.Is 139720 divisible by 20?
  34. 34.Is 49237 divisible by 8?
  35. 35.Is 105540 divisible by 30?
  36. 36.Is 10179 divisible by 2?
  37. 37.Is 81593 divisible by 19?
  38. 38.Is 68220 divisible by 15?
  39. 39.Is 23672 divisible by 4?
  40. 40.Is 58828 divisible by 11?

Answer key

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

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