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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 296 · 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 17408 divisible by 17?
  2. 2.Is 145639 divisible by 23?
  3. 3.Is 31836 divisible by 6?
  4. 4.Is 6258 divisible by 7?
  5. 5.Is 98403 divisible by 24?
  6. 6.Is 24293 divisible by 17?
  7. 7.Is 78192 divisible by 24?
  8. 8.Is 1844 divisible by 3?
  9. 9.Is 68245 divisible by 10?
  10. 10.Is 126795 divisible by 19?
  11. 11.Is 21480 divisible by 12?
  12. 12.Is 4998 divisible by 6?
  13. 13.Is 88176 divisible by 24?
  14. 14.Is 79379 divisible by 20?
  15. 15.Is 32826 divisible by 30?
  16. 16.Is 1715 divisible by 5?
  17. 17.Is 17100 divisible by 3?
  18. 18.Is 1006 divisible by 8?
  19. 19.Is 15226 divisible by 6?
  20. 20.Is 121008 divisible by 24?
  21. 21.Is 7212 divisible by 12?
  22. 22.Is 193470 divisible by 30?
  23. 23.Is 43148 divisible by 23?
  24. 24.Is 1351 divisible by 2?
  25. 25.Is 29250 divisible by 10?
  26. 26.Is 41227 divisible by 7?
  27. 27.Is 5448 divisible by 6?
  28. 28.Is 52632 divisible by 9?
  29. 29.Is 11960 divisible by 20?
  30. 30.Is 100748 divisible by 15?
  31. 31.Is 2265 divisible by 2?
  32. 32.Is 10515 divisible by 12?
  33. 33.Is 73714 divisible by 23?
  34. 34.Is 21691 divisible by 11?
  35. 35.Is 15078 divisible by 7?
  36. 36.Is 47904 divisible by 8?
  37. 37.Is 55386 divisible by 9?
  38. 38.Is 10270 divisible by 3?
  39. 39.Is 40749 divisible by 12?
  40. 40.Is 198714 divisible by 30?

Answer key

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

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