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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 458 · 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 25195 divisible by 4?
  2. 2.Is 95095 divisible by 19?
  3. 3.Is 74736 divisible by 12?
  4. 4.Is 11445 divisible by 6?
  5. 5.Is 36801 divisible by 29?
  6. 6.Is 29278 divisible by 6?
  7. 7.Is 4705 divisible by 13?
  8. 8.Is 35485 divisible by 10?
  9. 9.Is 8271 divisible by 4?
  10. 10.Is 80527 divisible by 15?
  11. 11.Is 40346 divisible by 11?
  12. 12.Is 2034 divisible by 6?
  13. 13.Is 26400 divisible by 10?
  14. 14.Is 28957 divisible by 23?
  15. 15.Is 22476 divisible by 9?
  16. 16.Is 57126 divisible by 24?
  17. 17.Is 11031 divisible by 12?
  18. 18.Is 65197 divisible by 13?
  19. 19.Is 63638 divisible by 15?
  20. 20.Is 11960 divisible by 5?
  21. 21.Is 23976 divisible by 24?
  22. 22.Is 16360 divisible by 10?
  23. 23.Is 94170 divisible by 30?
  24. 24.Is 24710 divisible by 7?
  25. 25.Is 24094 divisible by 4?
  26. 26.Is 146439 divisible by 23?
  27. 27.Is 48525 divisible by 8?
  28. 28.Is 26443 divisible by 11?
  29. 29.Is 38967 divisible by 7?
  30. 30.Is 6960 divisible by 24?
  31. 31.Is 2943 divisible by 12?
  32. 32.Is 20989 divisible by 5?
  33. 33.Is 16319 divisible by 9?
  34. 34.Is 6781 divisible by 2?
  35. 35.Is 47965 divisible by 13?
  36. 36.Is 72753 divisible by 11?
  37. 37.Is 19322 divisible by 30?
  38. 38.Is 8664 divisible by 24?
  39. 39.Is 6264 divisible by 4?
  40. 40.Is 40334 divisible by 7?

Answer key

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

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