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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 444 · 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 31584 divisible by 5?
  2. 2.Is 16182 divisible by 29?
  3. 3.Is 41195 divisible by 6?
  4. 4.Is 27550 divisible by 19?
  5. 5.Is 37695 divisible by 7?
  6. 6.Is 9592 divisible by 9?
  7. 7.Is 20755 divisible by 17?
  8. 8.Is 88991 divisible by 23?
  9. 9.Is 3192 divisible by 24?
  10. 10.Is 1170 divisible by 13?
  11. 11.Is 13081 divisible by 9?
  12. 12.Is 6010 divisible by 5?
  13. 13.Is 17338 divisible by 30?
  14. 14.Is 5562 divisible by 3?
  15. 15.Is 93369 divisible by 18?
  16. 16.Is 36000 divisible by 9?
  17. 17.Is 17311 divisible by 17?
  18. 18.Is 12948 divisible by 4?
  19. 19.Is 13985 divisible by 3?
  20. 20.Is 54351 divisible by 9?
  21. 21.Is 148512 divisible by 24?
  22. 22.Is 9878 divisible by 13?
  23. 23.Is 6309 divisible by 4?
  24. 24.Is 119616 divisible by 24?
  25. 25.Is 18717 divisible by 7?
  26. 26.Is 1321 divisible by 5?
  27. 27.Is 14002 divisible by 30?
  28. 28.Is 108102 divisible by 18?
  29. 29.Is 32394 divisible by 24?
  30. 30.Is 26248 divisible by 17?
  31. 31.Is 129101 divisible by 20?
  32. 32.Is 78816 divisible by 12?
  33. 33.Is 1117 divisible by 2?
  34. 34.Is 1462 divisible by 15?
  35. 35.Is 31753 divisible by 6?
  36. 36.Is 84762 divisible by 18?
  37. 37.Is 33575 divisible by 19?
  38. 38.Is 69432 divisible by 24?
  39. 39.Is 16505 divisible by 5?
  40. 40.Is 14400 divisible by 5?

Answer key

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

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