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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 952 · 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 40230 divisible by 18?
  2. 2.Is 19822 divisible by 11?
  3. 3.Is 163598 divisible by 24?
  4. 4.Is 84681 divisible by 13?
  5. 5.Is 3053 divisible by 4?
  6. 6.Is 43199 divisible by 24?
  7. 7.Is 93404 divisible by 19?
  8. 8.Is 30077 divisible by 11?
  9. 9.Is 173702 divisible by 29?
  10. 10.Is 32160 divisible by 19?
  11. 11.Is 18488 divisible by 12?
  12. 12.Is 23343 divisible by 11?
  13. 13.Is 54448 divisible by 20?
  14. 14.Is 10291 divisible by 3?
  15. 15.Is 66165 divisible by 23?
  16. 16.Is 80505 divisible by 23?
  17. 17.Is 161904 divisible by 24?
  18. 18.Is 52211 divisible by 29?
  19. 19.Is 89640 divisible by 29?
  20. 20.Is 39670 divisible by 15?
  21. 21.Is 49515 divisible by 11?
  22. 22.Is 40130 divisible by 6?
  23. 23.Is 23866 divisible by 6?
  24. 24.Is 65640 divisible by 10?
  25. 25.Is 1610 divisible by 23?
  26. 26.Is 20681 divisible by 9?
  27. 27.Is 2595 divisible by 7?
  28. 28.Is 111022 divisible by 19?
  29. 29.Is 14888 divisible by 4?
  30. 30.Is 22078 divisible by 19?
  31. 31.Is 693 divisible by 2?
  32. 32.Is 58155 divisible by 10?
  33. 33.Is 37234 divisible by 17?
  34. 34.Is 6630 divisible by 15?
  35. 35.Is 31348 divisible by 8?
  36. 36.Is 5235 divisible by 2?
  37. 37.Is 126652 divisible by 29?
  38. 38.Is 96195 divisible by 15?
  39. 39.Is 22111 divisible by 4?
  40. 40.Is 154731 divisible by 30?

Answer key

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

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