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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 340 · 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 16242 divisible by 7?
  2. 2.Is 18355 divisible by 5?
  3. 3.Is 37272 divisible by 7?
  4. 4.Is 65030 divisible by 13?
  5. 5.Is 150980 divisible by 29?
  6. 6.Is 56890 divisible by 29?
  7. 7.Is 17670 divisible by 19?
  8. 8.Is 54591 divisible by 12?
  9. 9.Is 33064 divisible by 23?
  10. 10.Is 28938 divisible by 15?
  11. 11.Is 22684 divisible by 17?
  12. 12.Is 14885 divisible by 5?
  13. 13.Is 78720 divisible by 17?
  14. 14.Is 40509 divisible by 10?
  15. 15.Is 32978 divisible by 12?
  16. 16.Is 109345 divisible by 23?
  17. 17.Is 135287 divisible by 30?
  18. 18.Is 24820 divisible by 5?
  19. 19.Is 10699 divisible by 2?
  20. 20.Is 11557 divisible by 7?
  21. 21.Is 16164 divisible by 18?
  22. 22.Is 3532 divisible by 4?
  23. 23.Is 22920 divisible by 15?
  24. 24.Is 32852 divisible by 5?
  25. 25.Is 29241 divisible by 9?
  26. 26.Is 110934 divisible by 20?
  27. 27.Is 2576 divisible by 23?
  28. 28.Is 714 divisible by 12?
  29. 29.Is 56952 divisible by 9?
  30. 30.Is 505 divisible by 4?
  31. 31.Is 111688 divisible by 20?
  32. 32.Is 92053 divisible by 17?
  33. 33.Is 4046 divisible by 6?
  34. 34.Is 13563 divisible by 3?
  35. 35.Is 105830 divisible by 19?
  36. 36.Is 22842 divisible by 18?
  37. 37.Is 47467 divisible by 9?
  38. 38.Is 24935 divisible by 7?
  39. 39.Is 20761 divisible by 6?
  40. 40.Is 54454 divisible by 19?

Answer key

  1. no
  2. yes
  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. no
  16. no
  17. no
  18. yes
  19. no
  20. yes
  21. yes
  22. yes
  23. yes
  24. no
  25. yes
  26. no
  27. yes
  28. no
  29. yes
  30. no
  31. no
  32. no
  33. no
  34. yes
  35. yes
  36. yes
  37. no
  38. no
  39. no
  40. yes

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