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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 540 · 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 144992 divisible by 23?
  2. 2.Is 12910 divisible by 2?
  3. 3.Is 36656 divisible by 8?
  4. 4.Is 26922 divisible by 19?
  5. 5.Is 73169 divisible by 11?
  6. 6.Is 72254 divisible by 13?
  7. 7.Is 136822 divisible by 29?
  8. 8.Is 48734 divisible by 12?
  9. 9.Is 94854 divisible by 18?
  10. 10.Is 6744 divisible by 6?
  11. 11.Is 56344 divisible by 24?
  12. 12.Is 81152 divisible by 19?
  13. 13.Is 105660 divisible by 30?
  14. 14.Is 38550 divisible by 30?
  15. 15.Is 56699 divisible by 17?
  16. 16.Is 7689 divisible by 3?
  17. 17.Is 69274 divisible by 19?
  18. 18.Is 168635 divisible by 29?
  19. 19.Is 24811 divisible by 18?
  20. 20.Is 17260 divisible by 5?
  21. 21.Is 1807 divisible by 3?
  22. 22.Is 27056 divisible by 4?
  23. 23.Is 12328 divisible by 8?
  24. 24.Is 37642 divisible by 10?
  25. 25.Is 18415 divisible by 29?
  26. 26.Is 58950 divisible by 10?
  27. 27.Is 6228 divisible by 18?
  28. 28.Is 25770 divisible by 5?
  29. 29.Is 40310 divisible by 29?
  30. 30.Is 77564 divisible by 12?
  31. 31.Is 82922 divisible by 23?
  32. 32.Is 30461 divisible by 15?
  33. 33.Is 62124 divisible by 29?
  34. 34.Is 1999 divisible by 2?
  35. 35.Is 11188 divisible by 4?
  36. 36.Is 46552 divisible by 23?
  37. 37.Is 3934 divisible by 2?
  38. 38.Is 46960 divisible by 8?
  39. 39.Is 8207 divisible by 3?
  40. 40.Is 30488 divisible by 20?

Answer key

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

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