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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 14 · 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 58090 divisible by 10?
  2. 2.Is 56615 divisible by 13?
  3. 3.Is 98013 divisible by 20?
  4. 4.Is 104420 divisible by 23?
  5. 5.Is 18596 divisible by 6?
  6. 6.Is 6944 divisible by 8?
  7. 7.Is 38723 divisible by 13?
  8. 8.Is 22858 divisible by 11?
  9. 9.Is 13104 divisible by 9?
  10. 10.Is 98508 divisible by 29?
  11. 11.Is 25749 divisible by 4?
  12. 12.Is 53108 divisible by 11?
  13. 13.Is 9676 divisible by 4?
  14. 14.Is 147629 divisible by 29?
  15. 15.Is 65382 divisible by 15?
  16. 16.Is 15946 divisible by 24?
  17. 17.Is 136248 divisible by 24?
  18. 18.Is 6251 divisible by 19?
  19. 19.Is 17371 divisible by 3?
  20. 20.Is 3951 divisible by 5?
  21. 21.Is 11404 divisible by 2?
  22. 22.Is 3922 divisible by 2?
  23. 23.Is 17653 divisible by 3?
  24. 24.Is 31558 divisible by 12?
  25. 25.Is 27612 divisible by 4?
  26. 26.Is 36846 divisible by 9?
  27. 27.Is 48364 divisible by 12?
  28. 28.Is 48294 divisible by 7?
  29. 29.Is 18716 divisible by 4?
  30. 30.Is 104725 divisible by 20?
  31. 31.Is 5040 divisible by 10?
  32. 32.Is 20170 divisible by 10?
  33. 33.Is 15701 divisible by 13?
  34. 34.Is 56465 divisible by 23?
  35. 35.Is 29236 divisible by 7?
  36. 36.Is 11712 divisible by 8?
  37. 37.Is 45464 divisible by 8?
  38. 38.Is 7218 divisible by 4?
  39. 39.Is 59990 divisible by 19?
  40. 40.Is 38983 divisible by 17?

Answer key

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

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