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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 97 · 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 2857 divisible by 6?
  2. 2.Is 149225 divisible by 23?
  3. 3.Is 30700 divisible by 20?
  4. 4.Is 28950 divisible by 5?
  5. 5.Is 32093 divisible by 24?
  6. 6.Is 110587 divisible by 20?
  7. 7.Is 98718 divisible by 24?
  8. 8.Is 13048 divisible by 2?
  9. 9.Is 182721 divisible by 29?
  10. 10.Is 15708 divisible by 3?
  11. 11.Is 15123 divisible by 4?
  12. 12.Is 99761 divisible by 19?
  13. 13.Is 103268 divisible by 24?
  14. 14.Is 37368 divisible by 12?
  15. 15.Is 39740 divisible by 18?
  16. 16.Is 4926 divisible by 3?
  17. 17.Is 50071 divisible by 23?
  18. 18.Is 8796 divisible by 12?
  19. 19.Is 9614 divisible by 19?
  20. 20.Is 49202 divisible by 12?
  21. 21.Is 12855 divisible by 15?
  22. 22.Is 23205 divisible by 17?
  23. 23.Is 41929 divisible by 8?
  24. 24.Is 8941 divisible by 2?
  25. 25.Is 47 divisible by 3?
  26. 26.Is 16948 divisible by 19?
  27. 27.Is 13229 divisible by 2?
  28. 28.Is 190994 divisible by 30?
  29. 29.Is 94115 divisible by 29?
  30. 30.Is 62670 divisible by 15?
  31. 31.Is 9900 divisible by 20?
  32. 32.Is 30346 divisible by 5?
  33. 33.Is 41766 divisible by 6?
  34. 34.Is 21248 divisible by 4?
  35. 35.Is 23452 divisible by 8?
  36. 36.Is 49394 divisible by 9?
  37. 37.Is 59505 divisible by 17?
  38. 38.Is 41088 divisible by 10?
  39. 39.Is 116300 divisible by 17?
  40. 40.Is 38600 divisible by 19?

Answer key

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

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