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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 2 · 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 73546 divisible by 15?
  2. 2.Is 93374 divisible by 29?
  3. 3.Is 31963 divisible by 17?
  4. 4.Is 114085 divisible by 30?
  5. 5.Is 41404 divisible by 13?
  6. 6.Is 16177 divisible by 3?
  7. 7.Is 63120 divisible by 15?
  8. 8.Is 13077 divisible by 4?
  9. 9.Is 96112 divisible by 24?
  10. 10.Is 44830 divisible by 12?
  11. 11.Is 17503 divisible by 5?
  12. 12.Is 202275 divisible by 29?
  13. 13.Is 69341 divisible by 11?
  14. 14.Is 64281 divisible by 24?
  15. 15.Is 176 divisible by 2?
  16. 16.Is 63825 divisible by 23?
  17. 17.Is 106470 divisible by 30?
  18. 18.Is 5889 divisible by 13?
  19. 19.Is 14724 divisible by 12?
  20. 20.Is 95520 divisible by 15?
  21. 21.Is 62248 divisible by 11?
  22. 22.Is 63792 divisible by 24?
  23. 23.Is 4930 divisible by 3?
  24. 24.Is 10590 divisible by 30?
  25. 25.Is 9255 divisible by 4?
  26. 26.Is 115045 divisible by 20?
  27. 27.Is 19834 divisible by 20?
  28. 28.Is 6566 divisible by 6?
  29. 29.Is 33006 divisible by 7?
  30. 30.Is 107388 divisible by 19?
  31. 31.Is 54625 divisible by 19?
  32. 32.Is 133435 divisible by 24?
  33. 33.Is 46381 divisible by 19?
  34. 34.Is 15660 divisible by 29?
  35. 35.Is 73397 divisible by 19?
  36. 36.Is 38060 divisible by 6?
  37. 37.Is 68310 divisible by 18?
  38. 38.Is 45618 divisible by 8?
  39. 39.Is 73350 divisible by 13?
  40. 40.Is 8955 divisible by 4?

Answer key

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

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