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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 784 · 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 106380 divisible by 20?
  2. 2.Is 18360 divisible by 30?
  3. 3.Is 39835 divisible by 10?
  4. 4.Is 20808 divisible by 3?
  5. 5.Is 40576 divisible by 8?
  6. 6.Is 1972 divisible by 6?
  7. 7.Is 139374 divisible by 29?
  8. 8.Is 1949 divisible by 4?
  9. 9.Is 90343 divisible by 24?
  10. 10.Is 6878 divisible by 19?
  11. 11.Is 5795 divisible by 5?
  12. 12.Is 48527 divisible by 11?
  13. 13.Is 3135 divisible by 2?
  14. 14.Is 65637 divisible by 17?
  15. 15.Is 52530 divisible by 15?
  16. 16.Is 21335 divisible by 10?
  17. 17.Is 32118 divisible by 6?
  18. 18.Is 88923 divisible by 20?
  19. 19.Is 77197 divisible by 17?
  20. 20.Is 22050 divisible by 20?
  21. 21.Is 59983 divisible by 13?
  22. 22.Is 191670 divisible by 30?
  23. 23.Is 67601 divisible by 24?
  24. 24.Is 70069 divisible by 18?
  25. 25.Is 78811 divisible by 12?
  26. 26.Is 33994 divisible by 23?
  27. 27.Is 15395 divisible by 4?
  28. 28.Is 16187 divisible by 6?
  29. 29.Is 18904 divisible by 3?
  30. 30.Is 11394 divisible by 18?
  31. 31.Is 6814 divisible by 7?
  32. 32.Is 4993 divisible by 3?
  33. 33.Is 35224 divisible by 11?
  34. 34.Is 7642 divisible by 7?
  35. 35.Is 26568 divisible by 6?
  36. 36.Is 99403 divisible by 18?
  37. 37.Is 9759 divisible by 2?
  38. 38.Is 53559 divisible by 29?
  39. 39.Is 1820 divisible by 4?
  40. 40.Is 16041 divisible by 19?

Answer key

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

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