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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 248 · 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 7616 divisible by 5?
  2. 2.Is 91724 divisible by 23?
  3. 3.Is 5739 divisible by 3?
  4. 4.Is 14254 divisible by 11?
  5. 5.Is 122884 divisible by 19?
  6. 6.Is 24493 divisible by 7?
  7. 7.Is 38584 divisible by 7?
  8. 8.Is 122611 divisible by 29?
  9. 9.Is 73601 divisible by 11?
  10. 10.Is 112380 divisible by 20?
  11. 11.Is 10386 divisible by 3?
  12. 12.Is 107502 divisible by 23?
  13. 13.Is 25970 divisible by 7?
  14. 14.Is 25948 divisible by 20?
  15. 15.Is 616 divisible by 11?
  16. 16.Is 54510 divisible by 30?
  17. 17.Is 47541 divisible by 9?
  18. 18.Is 23778 divisible by 4?
  19. 19.Is 24263 divisible by 20?
  20. 20.Is 118146 divisible by 29?
  21. 21.Is 68412 divisible by 15?
  22. 22.Is 46230 divisible by 30?
  23. 23.Is 59425 divisible by 15?
  24. 24.Is 49590 divisible by 15?
  25. 25.Is 46830 divisible by 7?
  26. 26.Is 45513 divisible by 9?
  27. 27.Is 86969 divisible by 18?
  28. 28.Is 35192 divisible by 13?
  29. 29.Is 128035 divisible by 29?
  30. 30.Is 169879 divisible by 30?
  31. 31.Is 4826 divisible by 5?
  32. 32.Is 10612 divisible by 4?
  33. 33.Is 19527 divisible by 3?
  34. 34.Is 30604 divisible by 15?
  35. 35.Is 10530 divisible by 10?
  36. 36.Is 40361 divisible by 12?
  37. 37.Is 9732 divisible by 3?
  38. 38.Is 3736 divisible by 19?
  39. 39.Is 33560 divisible by 19?
  40. 40.Is 112800 divisible by 30?

Answer key

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

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