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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 652 · 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 9591 divisible by 11?
  2. 2.Is 190269 divisible by 29?
  3. 3.Is 8330 divisible by 11?
  4. 4.Is 4575 divisible by 2?
  5. 5.Is 60 divisible by 3?
  6. 6.Is 1017 divisible by 2?
  7. 7.Is 69874 divisible by 23?
  8. 8.Is 11930 divisible by 13?
  9. 9.Is 45481 divisible by 8?
  10. 10.Is 7199 divisible by 2?
  11. 11.Is 57560 divisible by 20?
  12. 12.Is 714 divisible by 6?
  13. 13.Is 17273 divisible by 7?
  14. 14.Is 20712 divisible by 8?
  15. 15.Is 40187 divisible by 13?
  16. 16.Is 101507 divisible by 15?
  17. 17.Is 4602 divisible by 3?
  18. 18.Is 13396 divisible by 5?
  19. 19.Is 21103 divisible by 6?
  20. 20.Is 157439 divisible by 30?
  21. 21.Is 16059 divisible by 3?
  22. 22.Is 68337 divisible by 15?
  23. 23.Is 28416 divisible by 12?
  24. 24.Is 33240 divisible by 30?
  25. 25.Is 12307 divisible by 3?
  26. 26.Is 60460 divisible by 10?
  27. 27.Is 64494 divisible by 17?
  28. 28.Is 55590 divisible by 15?
  29. 29.Is 28020 divisible by 15?
  30. 30.Is 18237 divisible by 7?
  31. 31.Is 108813 divisible by 19?
  32. 32.Is 76967 divisible by 18?
  33. 33.Is 89077 divisible by 29?
  34. 34.Is 12280 divisible by 3?
  35. 35.Is 152804 divisible by 30?
  36. 36.Is 5582 divisible by 6?
  37. 37.Is 47223 divisible by 9?
  38. 38.Is 37254 divisible by 6?
  39. 39.Is 58923 divisible by 20?
  40. 40.Is 113840 divisible by 20?

Answer key

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

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