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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 59 · 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 195112 divisible by 29?
  2. 2.Is 5697 divisible by 2?
  3. 3.Is 111251 divisible by 20?
  4. 4.Is 41323 divisible by 20?
  5. 5.Is 21113 divisible by 4?
  6. 6.Is 17678 divisible by 29?
  7. 7.Is 40800 divisible by 24?
  8. 8.Is 33916 divisible by 7?
  9. 9.Is 23712 divisible by 12?
  10. 10.Is 3542 divisible by 11?
  11. 11.Is 126279 divisible by 30?
  12. 12.Is 204794 divisible by 30?
  13. 13.Is 8595 divisible by 15?
  14. 14.Is 29155 divisible by 5?
  15. 15.Is 43288 divisible by 23?
  16. 16.Is 37307 divisible by 8?
  17. 17.Is 9639 divisible by 7?
  18. 18.Is 38309 divisible by 29?
  19. 19.Is 31901 divisible by 19?
  20. 20.Is 52364 divisible by 19?
  21. 21.Is 11211 divisible by 3?
  22. 22.Is 28500 divisible by 10?
  23. 23.Is 70244 divisible by 12?
  24. 24.Is 26802 divisible by 5?
  25. 25.Is 5915 divisible by 7?
  26. 26.Is 15552 divisible by 3?
  27. 27.Is 14022 divisible by 18?
  28. 28.Is 10339 divisible by 7?
  29. 29.Is 13374 divisible by 6?
  30. 30.Is 22643 divisible by 30?
  31. 31.Is 10707 divisible by 30?
  32. 32.Is 22140 divisible by 4?
  33. 33.Is 37508 divisible by 12?
  34. 34.Is 114012 divisible by 18?
  35. 35.Is 18700 divisible by 11?
  36. 36.Is 15363 divisible by 3?
  37. 37.Is 14453 divisible by 6?
  38. 38.Is 90685 divisible by 20?
  39. 39.Is 28912 divisible by 8?
  40. 40.Is 2552 divisible by 8?

Answer key

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

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