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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 905 · 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 470 divisible by 2?
  2. 2.Is 32915 divisible by 5?
  3. 3.Is 128140 divisible by 24?
  4. 4.Is 32220 divisible by 29?
  5. 5.Is 7237 divisible by 8?
  6. 6.Is 2172 divisible by 7?
  7. 7.Is 109967 divisible by 17?
  8. 8.Is 116369 divisible by 23?
  9. 9.Is 1535 divisible by 2?
  10. 10.Is 11772 divisible by 6?
  11. 11.Is 15913 divisible by 11?
  12. 12.Is 13939 divisible by 12?
  13. 13.Is 74328 divisible by 19?
  14. 14.Is 179209 divisible by 30?
  15. 15.Is 30474 divisible by 18?
  16. 16.Is 41511 divisible by 7?
  17. 17.Is 14244 divisible by 15?
  18. 18.Is 68192 divisible by 10?
  19. 19.Is 44670 divisible by 15?
  20. 20.Is 2943 divisible by 8?
  21. 21.Is 22624 divisible by 8?
  22. 22.Is 39199 divisible by 12?
  23. 23.Is 8932 divisible by 8?
  24. 24.Is 42800 divisible by 10?
  25. 25.Is 40957 divisible by 7?
  26. 26.Is 9914 divisible by 7?
  27. 27.Is 88392 divisible by 29?
  28. 28.Is 20305 divisible by 17?
  29. 29.Is 55008 divisible by 24?
  30. 30.Is 12155 divisible by 23?
  31. 31.Is 25018 divisible by 5?
  32. 32.Is 13420 divisible by 7?
  33. 33.Is 1518 divisible by 3?
  34. 34.Is 26881 divisible by 6?
  35. 35.Is 34803 divisible by 10?
  36. 36.Is 49647 divisible by 13?
  37. 37.Is 101660 divisible by 23?
  38. 38.Is 7840 divisible by 17?
  39. 39.Is 7799 divisible by 4?
  40. 40.Is 61149 divisible by 10?

Answer key

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

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