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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 156 · 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 66875 divisible by 13?
  2. 2.Is 15326 divisible by 12?
  3. 3.Is 38485 divisible by 17?
  4. 4.Is 22000 divisible by 19?
  5. 5.Is 114431 divisible by 18?
  6. 6.Is 59859 divisible by 12?
  7. 7.Is 6061 divisible by 19?
  8. 8.Is 17160 divisible by 6?
  9. 9.Is 74151 divisible by 29?
  10. 10.Is 26734 divisible by 11?
  11. 11.Is 1586 divisible by 13?
  12. 12.Is 28440 divisible by 5?
  13. 13.Is 177870 divisible by 30?
  14. 14.Is 1221 divisible by 6?
  15. 15.Is 43162 divisible by 7?
  16. 16.Is 47112 divisible by 7?
  17. 17.Is 33822 divisible by 6?
  18. 18.Is 103736 divisible by 20?
  19. 19.Is 36816 divisible by 13?
  20. 20.Is 9702 divisible by 11?
  21. 21.Is 120150 divisible by 30?
  22. 22.Is 104260 divisible by 20?
  23. 23.Is 3970 divisible by 15?
  24. 24.Is 14667 divisible by 6?
  25. 25.Is 22692 divisible by 6?
  26. 26.Is 1365 divisible by 3?
  27. 27.Is 12072 divisible by 2?
  28. 28.Is 66482 divisible by 18?
  29. 29.Is 73407 divisible by 13?
  30. 30.Is 96154 divisible by 17?
  31. 31.Is 10099 divisible by 2?
  32. 32.Is 7295 divisible by 7?
  33. 33.Is 77168 divisible by 13?
  34. 34.Is 10825 divisible by 29?
  35. 35.Is 89927 divisible by 19?
  36. 36.Is 113860 divisible by 18?
  37. 37.Is 2184 divisible by 3?
  38. 38.Is 37342 divisible by 20?
  39. 39.Is 54711 divisible by 9?
  40. 40.Is 39899 divisible by 6?

Answer key

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

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