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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 181 · 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 60054 divisible by 17?
  2. 2.Is 13864 divisible by 2?
  3. 3.Is 39090 divisible by 10?
  4. 4.Is 24320 divisible by 10?
  5. 5.Is 40486 divisible by 7?
  6. 6.Is 50218 divisible by 17?
  7. 7.Is 41057 divisible by 19?
  8. 8.Is 17072 divisible by 12?
  9. 9.Is 50425 divisible by 15?
  10. 10.Is 42009 divisible by 10?
  11. 11.Is 137634 divisible by 29?
  12. 12.Is 22944 divisible by 8?
  13. 13.Is 642 divisible by 19?
  14. 14.Is 93894 divisible by 23?
  15. 15.Is 125590 divisible by 19?
  16. 16.Is 77199 divisible by 18?
  17. 17.Is 114718 divisible by 23?
  18. 18.Is 35865 divisible by 9?
  19. 19.Is 10150 divisible by 3?
  20. 20.Is 72780 divisible by 15?
  21. 21.Is 11791 divisible by 5?
  22. 22.Is 26224 divisible by 8?
  23. 23.Is 88349 divisible by 29?
  24. 24.Is 38360 divisible by 20?
  25. 25.Is 67140 divisible by 20?
  26. 26.Is 12179 divisible by 17?
  27. 27.Is 27170 divisible by 7?
  28. 28.Is 42714 divisible by 7?
  29. 29.Is 10425 divisible by 7?
  30. 30.Is 61497 divisible by 19?
  31. 31.Is 75495 divisible by 15?
  32. 32.Is 11769 divisible by 2?
  33. 33.Is 14262 divisible by 8?
  34. 34.Is 35595 divisible by 13?
  35. 35.Is 49967 divisible by 29?
  36. 36.Is 22965 divisible by 23?
  37. 37.Is 92392 divisible by 18?
  38. 38.Is 78812 divisible by 19?
  39. 39.Is 13069 divisible by 7?
  40. 40.Is 71923 divisible by 13?

Answer key

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

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