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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 158 · 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 2627 divisible by 15?
  2. 2.Is 105821 divisible by 29?
  3. 3.Is 107477 divisible by 24?
  4. 4.Is 111938 divisible by 29?
  5. 5.Is 100500 divisible by 15?
  6. 6.Is 33879 divisible by 23?
  7. 7.Is 2462 divisible by 5?
  8. 8.Is 20937 divisible by 3?
  9. 9.Is 18570 divisible by 11?
  10. 10.Is 29829 divisible by 9?
  11. 11.Is 11610 divisible by 30?
  12. 12.Is 119124 divisible by 18?
  13. 13.Is 20860 divisible by 4?
  14. 14.Is 12340 divisible by 4?
  15. 15.Is 79220 divisible by 17?
  16. 16.Is 1189 divisible by 10?
  17. 17.Is 75930 divisible by 23?
  18. 18.Is 9219 divisible by 7?
  19. 19.Is 32243 divisible by 6?
  20. 20.Is 8884 divisible by 7?
  21. 21.Is 2027 divisible by 4?
  22. 22.Is 12319 divisible by 5?
  23. 23.Is 19824 divisible by 18?
  24. 24.Is 88500 divisible by 30?
  25. 25.Is 19530 divisible by 3?
  26. 26.Is 5841 divisible by 3?
  27. 27.Is 51634 divisible by 23?
  28. 28.Is 12534 divisible by 6?
  29. 29.Is 106430 divisible by 20?
  30. 30.Is 27240 divisible by 11?
  31. 31.Is 61399 divisible by 9?
  32. 32.Is 5813 divisible by 30?
  33. 33.Is 156262 divisible by 23?
  34. 34.Is 16285 divisible by 5?
  35. 35.Is 54752 divisible by 29?
  36. 36.Is 35455 divisible by 10?
  37. 37.Is 60841 divisible by 18?
  38. 38.Is 7231 divisible by 4?
  39. 39.Is 3266 divisible by 23?
  40. 40.Is 13645 divisible by 5?

Answer key

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

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