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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 365 · 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 24204 divisible by 12?
  2. 2.Is 19532 divisible by 19?
  3. 3.Is 44091 divisible by 11?
  4. 4.Is 12880 divisible by 4?
  5. 5.Is 14919 divisible by 3?
  6. 6.Is 123218 divisible by 24?
  7. 7.Is 10860 divisible by 10?
  8. 8.Is 49641 divisible by 18?
  9. 9.Is 39003 divisible by 20?
  10. 10.Is 8983 divisible by 2?
  11. 11.Is 19640 divisible by 10?
  12. 12.Is 44109 divisible by 29?
  13. 13.Is 18902 divisible by 5?
  14. 14.Is 29570 divisible by 5?
  15. 15.Is 70326 divisible by 18?
  16. 16.Is 2272 divisible by 10?
  17. 17.Is 33283 divisible by 7?
  18. 18.Is 26610 divisible by 6?
  19. 19.Is 45816 divisible by 24?
  20. 20.Is 37508 divisible by 24?
  21. 21.Is 13765 divisible by 2?
  22. 22.Is 2296 divisible by 7?
  23. 23.Is 32151 divisible by 24?
  24. 24.Is 65875 divisible by 19?
  25. 25.Is 140073 divisible by 24?
  26. 26.Is 13714 divisible by 15?
  27. 27.Is 6544 divisible by 5?
  28. 28.Is 19600 divisible by 8?
  29. 29.Is 112584 divisible by 24?
  30. 30.Is 38353 divisible by 30?
  31. 31.Is 84735 divisible by 15?
  32. 32.Is 93384 divisible by 20?
  33. 33.Is 171 divisible by 5?
  34. 34.Is 1902 divisible by 8?
  35. 35.Is 41922 divisible by 9?
  36. 36.Is 42639 divisible by 12?
  37. 37.Is 1596 divisible by 3?
  38. 38.Is 103224 divisible by 19?
  39. 39.Is 171448 divisible by 29?
  40. 40.Is 38058 divisible by 6?

Answer key

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

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