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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 284 · 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 44591 divisible by 8?
  2. 2.Is 66690 divisible by 13?
  3. 3.Is 77320 divisible by 18?
  4. 4.Is 1944 divisible by 5?
  5. 5.Is 111914 divisible by 30?
  6. 6.Is 1638 divisible by 6?
  7. 7.Is 14877 divisible by 6?
  8. 8.Is 67478 divisible by 18?
  9. 9.Is 126880 divisible by 20?
  10. 10.Is 82907 divisible by 13?
  11. 11.Is 17900 divisible by 6?
  12. 12.Is 8655 divisible by 2?
  13. 13.Is 7376 divisible by 11?
  14. 14.Is 25203 divisible by 17?
  15. 15.Is 32222 divisible by 8?
  16. 16.Is 33163 divisible by 13?
  17. 17.Is 35326 divisible by 9?
  18. 18.Is 3529 divisible by 4?
  19. 19.Is 7768 divisible by 17?
  20. 20.Is 39291 divisible by 7?
  21. 21.Is 19334 divisible by 3?
  22. 22.Is 4899 divisible by 23?
  23. 23.Is 105825 divisible by 30?
  24. 24.Is 99702 divisible by 30?
  25. 25.Is 46720 divisible by 20?
  26. 26.Is 43533 divisible by 7?
  27. 27.Is 6561 divisible by 11?
  28. 28.Is 23376 divisible by 8?
  29. 29.Is 14377 divisible by 4?
  30. 30.Is 7953 divisible by 6?
  31. 31.Is 35036 divisible by 13?
  32. 32.Is 89857 divisible by 30?
  33. 33.Is 47920 divisible by 10?
  34. 34.Is 46874 divisible by 23?
  35. 35.Is 69740 divisible by 10?
  36. 36.Is 47270 divisible by 29?
  37. 37.Is 50199 divisible by 11?
  38. 38.Is 69513 divisible by 13?
  39. 39.Is 35820 divisible by 20?
  40. 40.Is 7836 divisible by 23?

Answer key

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

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