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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 993 · 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 30536 divisible by 8?
  2. 2.Is 4902 divisible by 3?
  3. 3.Is 103110 divisible by 30?
  4. 4.Is 12650 divisible by 4?
  5. 5.Is 4970 divisible by 3?
  6. 6.Is 28612 divisible by 5?
  7. 7.Is 55947 divisible by 17?
  8. 8.Is 71716 divisible by 29?
  9. 9.Is 34560 divisible by 6?
  10. 10.Is 1863 divisible by 7?
  11. 11.Is 71438 divisible by 23?
  12. 12.Is 17948 divisible by 15?
  13. 13.Is 123985 divisible by 24?
  14. 14.Is 6573 divisible by 4?
  15. 15.Is 9966 divisible by 29?
  16. 16.Is 93042 divisible by 18?
  17. 17.Is 18851 divisible by 3?
  18. 18.Is 8230 divisible by 5?
  19. 19.Is 6731 divisible by 23?
  20. 20.Is 24840 divisible by 30?
  21. 21.Is 59347 divisible by 17?
  22. 22.Is 35268 divisible by 12?
  23. 23.Is 9517 divisible by 2?
  24. 24.Is 35516 divisible by 7?
  25. 25.Is 8352 divisible by 4?
  26. 26.Is 120759 divisible by 18?
  27. 27.Is 61491 divisible by 11?
  28. 28.Is 96245 divisible by 17?
  29. 29.Is 6035 divisible by 2?
  30. 30.Is 3775 divisible by 2?
  31. 31.Is 19741 divisible by 15?
  32. 32.Is 1502 divisible by 2?
  33. 33.Is 24269 divisible by 4?
  34. 34.Is 15838 divisible by 13?
  35. 35.Is 7545 divisible by 5?
  36. 36.Is 9188 divisible by 15?
  37. 37.Is 2633 divisible by 2?
  38. 38.Is 65685 divisible by 29?
  39. 39.Is 31328 divisible by 5?
  40. 40.Is 138815 divisible by 29?

Answer key

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

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