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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 516 · 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 115185 divisible by 19?
  2. 2.Is 126888 divisible by 20?
  3. 3.Is 46104 divisible by 12?
  4. 4.Is 43317 divisible by 9?
  5. 5.Is 21798 divisible by 9?
  6. 6.Is 35699 divisible by 29?
  7. 7.Is 8628 divisible by 3?
  8. 8.Is 88800 divisible by 15?
  9. 9.Is 57814 divisible by 29?
  10. 10.Is 24565 divisible by 17?
  11. 11.Is 25997 divisible by 6?
  12. 12.Is 92268 divisible by 20?
  13. 13.Is 81840 divisible by 12?
  14. 14.Is 43906 divisible by 29?
  15. 15.Is 6516 divisible by 18?
  16. 16.Is 91205 divisible by 29?
  17. 17.Is 79762 divisible by 20?
  18. 18.Is 4363 divisible by 10?
  19. 19.Is 46840 divisible by 10?
  20. 20.Is 88470 divisible by 13?
  21. 21.Is 34442 divisible by 17?
  22. 22.Is 142075 divisible by 29?
  23. 23.Is 65670 divisible by 11?
  24. 24.Is 42010 divisible by 8?
  25. 25.Is 37384 divisible by 29?
  26. 26.Is 36517 divisible by 24?
  27. 27.Is 133967 divisible by 20?
  28. 28.Is 152881 divisible by 23?
  29. 29.Is 48126 divisible by 20?
  30. 30.Is 10838 divisible by 4?
  31. 31.Is 141145 divisible by 23?
  32. 32.Is 33855 divisible by 15?
  33. 33.Is 4895 divisible by 2?
  34. 34.Is 80973 divisible by 15?
  35. 35.Is 98362 divisible by 17?
  36. 36.Is 32544 divisible by 20?
  37. 37.Is 17120 divisible by 9?
  38. 38.Is 18855 divisible by 15?
  39. 39.Is 146947 divisible by 23?
  40. 40.Is 18774 divisible by 19?

Answer key

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

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