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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 154 · 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 64549 divisible by 19?
  2. 2.Is 81858 divisible by 30?
  3. 3.Is 32304 divisible by 24?
  4. 4.Is 167 divisible by 2?
  5. 5.Is 12796 divisible by 24?
  6. 6.Is 59892 divisible by 11?
  7. 7.Is 47414 divisible by 20?
  8. 8.Is 2568 divisible by 3?
  9. 9.Is 3165 divisible by 2?
  10. 10.Is 27681 divisible by 9?
  11. 11.Is 12418 divisible by 7?
  12. 12.Is 100037 divisible by 20?
  13. 13.Is 3896 divisible by 3?
  14. 14.Is 58225 divisible by 10?
  15. 15.Is 33495 divisible by 6?
  16. 16.Is 4993 divisible by 6?
  17. 17.Is 7914 divisible by 6?
  18. 18.Is 5286 divisible by 12?
  19. 19.Is 14153 divisible by 3?
  20. 20.Is 30380 divisible by 6?
  21. 21.Is 18709 divisible by 10?
  22. 22.Is 12839 divisible by 10?
  23. 23.Is 104907 divisible by 17?
  24. 24.Is 9715 divisible by 5?
  25. 25.Is 76725 divisible by 15?
  26. 26.Is 33569 divisible by 6?
  27. 27.Is 18320 divisible by 10?
  28. 28.Is 84862 divisible by 23?
  29. 29.Is 17044 divisible by 3?
  30. 30.Is 1036 divisible by 7?
  31. 31.Is 113568 divisible by 29?
  32. 32.Is 78996 divisible by 12?
  33. 33.Is 17310 divisible by 3?
  34. 34.Is 1212 divisible by 7?
  35. 35.Is 7344 divisible by 2?
  36. 36.Is 52290 divisible by 30?
  37. 37.Is 17097 divisible by 6?
  38. 38.Is 57816 divisible by 18?
  39. 39.Is 1809 divisible by 4?
  40. 40.Is 7340 divisible by 12?

Answer key

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

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