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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 499 · 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 28151 divisible by 10?
  2. 2.Is 4034 divisible by 2?
  3. 3.Is 36464 divisible by 11?
  4. 4.Is 145783 divisible by 30?
  5. 5.Is 35688 divisible by 13?
  6. 6.Is 23218 divisible by 13?
  7. 7.Is 9088 divisible by 4?
  8. 8.Is 83713 divisible by 23?
  9. 9.Is 9596 divisible by 3?
  10. 10.Is 38177 divisible by 23?
  11. 11.Is 24687 divisible by 15?
  12. 12.Is 24136 divisible by 8?
  13. 13.Is 78204 divisible by 23?
  14. 14.Is 55008 divisible by 19?
  15. 15.Is 12116 divisible by 4?
  16. 16.Is 39320 divisible by 20?
  17. 17.Is 38685 divisible by 15?
  18. 18.Is 36944 divisible by 15?
  19. 19.Is 22680 divisible by 7?
  20. 20.Is 3155 divisible by 8?
  21. 21.Is 6418 divisible by 2?
  22. 22.Is 84764 divisible by 18?
  23. 23.Is 49360 divisible by 8?
  24. 24.Is 27166 divisible by 17?
  25. 25.Is 202095 divisible by 30?
  26. 26.Is 66520 divisible by 18?
  27. 27.Is 125790 divisible by 30?
  28. 28.Is 8625 divisible by 3?
  29. 29.Is 27851 divisible by 10?
  30. 30.Is 24928 divisible by 8?
  31. 31.Is 27956 divisible by 4?
  32. 32.Is 15883 divisible by 7?
  33. 33.Is 7671 divisible by 6?
  34. 34.Is 106414 divisible by 18?
  35. 35.Is 5775 divisible by 7?
  36. 36.Is 28307 divisible by 8?
  37. 37.Is 27998 divisible by 13?
  38. 38.Is 2194 divisible by 4?
  39. 39.Is 29528 divisible by 6?
  40. 40.Is 84099 divisible by 13?

Answer key

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

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