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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 941 · 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 34266 divisible by 17?
  2. 2.Is 2980 divisible by 4?
  3. 3.Is 18357 divisible by 5?
  4. 4.Is 114028 divisible by 29?
  5. 5.Is 37375 divisible by 23?
  6. 6.Is 43420 divisible by 11?
  7. 7.Is 62586 divisible by 18?
  8. 8.Is 20828 divisible by 4?
  9. 9.Is 37013 divisible by 17?
  10. 10.Is 111090 divisible by 30?
  11. 11.Is 2824 divisible by 7?
  12. 12.Is 10300 divisible by 10?
  13. 13.Is 162782 divisible by 24?
  14. 14.Is 4718 divisible by 4?
  15. 15.Is 9512 divisible by 4?
  16. 16.Is 25060 divisible by 7?
  17. 17.Is 35027 divisible by 10?
  18. 18.Is 66608 divisible by 23?
  19. 19.Is 46296 divisible by 18?
  20. 20.Is 82352 divisible by 19?
  21. 21.Is 53604 divisible by 24?
  22. 22.Is 62500 divisible by 9?
  23. 23.Is 192 divisible by 4?
  24. 24.Is 71877 divisible by 13?
  25. 25.Is 5880 divisible by 6?
  26. 26.Is 47108 divisible by 8?
  27. 27.Is 27129 divisible by 5?
  28. 28.Is 44692 divisible by 11?
  29. 29.Is 16368 divisible by 8?
  30. 30.Is 19461 divisible by 17?
  31. 31.Is 124660 divisible by 23?
  32. 32.Is 27504 divisible by 6?
  33. 33.Is 31844 divisible by 12?
  34. 34.Is 53360 divisible by 10?
  35. 35.Is 57239 divisible by 13?
  36. 36.Is 143636 divisible by 24?
  37. 37.Is 62406 divisible by 9?
  38. 38.Is 30848 divisible by 8?
  39. 39.Is 760 divisible by 8?
  40. 40.Is 38116 divisible by 30?

Answer key

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

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