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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 809 · 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 24297 divisible by 13?
  2. 2.Is 32528 divisible by 19?
  3. 3.Is 90420 divisible by 30?
  4. 4.Is 9878 divisible by 4?
  5. 5.Is 87394 divisible by 13?
  6. 6.Is 30720 divisible by 8?
  7. 7.Is 73962 divisible by 12?
  8. 8.Is 31392 divisible by 8?
  9. 9.Is 17052 divisible by 8?
  10. 10.Is 80952 divisible by 12?
  11. 11.Is 114190 divisible by 19?
  12. 12.Is 12604 divisible by 3?
  13. 13.Is 99690 divisible by 15?
  14. 14.Is 98910 divisible by 18?
  15. 15.Is 20238 divisible by 7?
  16. 16.Is 45226 divisible by 9?
  17. 17.Is 89496 divisible by 18?
  18. 18.Is 51539 divisible by 12?
  19. 19.Is 47496 divisible by 12?
  20. 20.Is 97664 divisible by 15?
  21. 21.Is 30329 divisible by 6?
  22. 22.Is 10631 divisible by 23?
  23. 23.Is 39735 divisible by 19?
  24. 24.Is 12999 divisible by 6?
  25. 25.Is 13081 divisible by 4?
  26. 26.Is 33419 divisible by 5?
  27. 27.Is 58216 divisible by 19?
  28. 28.Is 14483 divisible by 3?
  29. 29.Is 23884 divisible by 4?
  30. 30.Is 94710 divisible by 30?
  31. 31.Is 14309 divisible by 9?
  32. 32.Is 133224 divisible by 24?
  33. 33.Is 47093 divisible by 8?
  34. 34.Is 49652 divisible by 10?
  35. 35.Is 27787 divisible by 6?
  36. 36.Is 28047 divisible by 19?
  37. 37.Is 27060 divisible by 6?
  38. 38.Is 1543 divisible by 3?
  39. 39.Is 195750 divisible by 30?
  40. 40.Is 69707 divisible by 18?

Answer key

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

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