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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 917 · 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 68608 divisible by 17?
  2. 2.Is 6910 divisible by 4?
  3. 3.Is 172445 divisible by 29?
  4. 4.Is 40062 divisible by 6?
  5. 5.Is 1455 divisible by 9?
  6. 6.Is 70812 divisible by 12?
  7. 7.Is 22047 divisible by 17?
  8. 8.Is 14102 divisible by 11?
  9. 9.Is 75748 divisible by 29?
  10. 10.Is 357 divisible by 2?
  11. 11.Is 36091 divisible by 23?
  12. 12.Is 191835 divisible by 29?
  13. 13.Is 17970 divisible by 6?
  14. 14.Is 17420 divisible by 5?
  15. 15.Is 4356 divisible by 3?
  16. 16.Is 10098 divisible by 11?
  17. 17.Is 228 divisible by 3?
  18. 18.Is 17998 divisible by 9?
  19. 19.Is 38208 divisible by 8?
  20. 20.Is 29195 divisible by 5?
  21. 21.Is 17254 divisible by 8?
  22. 22.Is 40883 divisible by 12?
  23. 23.Is 90200 divisible by 15?
  24. 24.Is 17258 divisible by 19?
  25. 25.Is 37992 divisible by 6?
  26. 26.Is 121200 divisible by 30?
  27. 27.Is 30354 divisible by 7?
  28. 28.Is 28217 divisible by 29?
  29. 29.Is 104546 divisible by 24?
  30. 30.Is 101441 divisible by 19?
  31. 31.Is 34936 divisible by 8?
  32. 32.Is 1219 divisible by 3?
  33. 33.Is 27289 divisible by 6?
  34. 34.Is 93172 divisible by 15?
  35. 35.Is 24667 divisible by 17?
  36. 36.Is 114048 divisible by 24?
  37. 37.Is 2180 divisible by 2?
  38. 38.Is 21712 divisible by 13?
  39. 39.Is 112407 divisible by 29?
  40. 40.Is 10187 divisible by 2?

Answer key

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

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