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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 728 · 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 23659 divisible by 29?
  2. 2.Is 38522 divisible by 11?
  3. 3.Is 188210 divisible by 29?
  4. 4.Is 147228 divisible by 23?
  5. 5.Is 5243 divisible by 2?
  6. 6.Is 40411 divisible by 9?
  7. 7.Is 98309 divisible by 29?
  8. 8.Is 139722 divisible by 29?
  9. 9.Is 9382 divisible by 6?
  10. 10.Is 137199 divisible by 29?
  11. 11.Is 21078 divisible by 5?
  12. 12.Is 55044 divisible by 11?
  13. 13.Is 45936 divisible by 29?
  14. 14.Is 25615 divisible by 17?
  15. 15.Is 7844 divisible by 6?
  16. 16.Is 74566 divisible by 13?
  17. 17.Is 35670 divisible by 29?
  18. 18.Is 206254 divisible by 30?
  19. 19.Is 47922 divisible by 7?
  20. 20.Is 68913 divisible by 19?
  21. 21.Is 95220 divisible by 18?
  22. 22.Is 2522 divisible by 13?
  23. 23.Is 526 divisible by 6?
  24. 24.Is 73210 divisible by 24?
  25. 25.Is 25955 divisible by 29?
  26. 26.Is 37078 divisible by 8?
  27. 27.Is 55745 divisible by 15?
  28. 28.Is 16513 divisible by 10?
  29. 29.Is 6924 divisible by 4?
  30. 30.Is 69680 divisible by 13?
  31. 31.Is 24420 divisible by 10?
  32. 32.Is 14877 divisible by 9?
  33. 33.Is 35001 divisible by 13?
  34. 34.Is 172342 divisible by 30?
  35. 35.Is 14433 divisible by 9?
  36. 36.Is 22912 divisible by 5?
  37. 37.Is 7301 divisible by 24?
  38. 38.Is 540 divisible by 4?
  39. 39.Is 37174 divisible by 10?
  40. 40.Is 6540 divisible by 2?

Answer key

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

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