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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 816 · 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 199424 divisible by 29?
  2. 2.Is 79791 divisible by 20?
  3. 3.Is 23436 divisible by 12?
  4. 4.Is 78918 divisible by 24?
  5. 5.Is 32520 divisible by 24?
  6. 6.Is 85098 divisible by 24?
  7. 7.Is 3810 divisible by 30?
  8. 8.Is 12948 divisible by 12?
  9. 9.Is 48900 divisible by 10?
  10. 10.Is 46026 divisible by 8?
  11. 11.Is 20088 divisible by 4?
  12. 12.Is 1563 divisible by 5?
  13. 13.Is 3074 divisible by 3?
  14. 14.Is 104546 divisible by 18?
  15. 15.Is 45672 divisible by 12?
  16. 16.Is 137952 divisible by 24?
  17. 17.Is 25389 divisible by 5?
  18. 18.Is 334 divisible by 12?
  19. 19.Is 14278 divisible by 11?
  20. 20.Is 9932 divisible by 12?
  21. 21.Is 75018 divisible by 12?
  22. 22.Is 1338 divisible by 3?
  23. 23.Is 58729 divisible by 19?
  24. 24.Is 50189 divisible by 23?
  25. 25.Is 146317 divisible by 24?
  26. 26.Is 70045 divisible by 11?
  27. 27.Is 31305 divisible by 5?
  28. 28.Is 42187 divisible by 17?
  29. 29.Is 24101 divisible by 5?
  30. 30.Is 84885 divisible by 15?
  31. 31.Is 13164 divisible by 6?
  32. 32.Is 18103 divisible by 9?
  33. 33.Is 147047 divisible by 24?
  34. 34.Is 29952 divisible by 18?
  35. 35.Is 2892 divisible by 2?
  36. 36.Is 4210 divisible by 17?
  37. 37.Is 77400 divisible by 15?
  38. 38.Is 6247 divisible by 13?
  39. 39.Is 1746 divisible by 9?
  40. 40.Is 4705 divisible by 2?

Answer key

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

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