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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 526 · 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 73036 divisible by 19?
  2. 2.Is 118658 divisible by 23?
  3. 3.Is 199607 divisible by 29?
  4. 4.Is 17020 divisible by 20?
  5. 5.Is 56745 divisible by 13?
  6. 6.Is 23454 divisible by 18?
  7. 7.Is 14439 divisible by 4?
  8. 8.Is 18821 divisible by 4?
  9. 9.Is 13150 divisible by 5?
  10. 10.Is 17400 divisible by 4?
  11. 11.Is 67160 divisible by 20?
  12. 12.Is 74949 divisible by 19?
  13. 13.Is 7219 divisible by 20?
  14. 14.Is 76826 divisible by 15?
  15. 15.Is 164343 divisible by 29?
  16. 16.Is 18318 divisible by 6?
  17. 17.Is 53663 divisible by 11?
  18. 18.Is 133974 divisible by 30?
  19. 19.Is 55251 divisible by 15?
  20. 20.Is 7215 divisible by 15?
  21. 21.Is 64070 divisible by 10?
  22. 22.Is 42990 divisible by 30?
  23. 23.Is 33309 divisible by 12?
  24. 24.Is 54573 divisible by 9?
  25. 25.Is 74850 divisible by 11?
  26. 26.Is 89850 divisible by 18?
  27. 27.Is 9056 divisible by 24?
  28. 28.Is 53066 divisible by 13?
  29. 29.Is 24106 divisible by 4?
  30. 30.Is 12540 divisible by 7?
  31. 31.Is 66370 divisible by 23?
  32. 32.Is 25141 divisible by 4?
  33. 33.Is 21965 divisible by 23?
  34. 34.Is 102420 divisible by 23?
  35. 35.Is 31405 divisible by 9?
  36. 36.Is 160630 divisible by 30?
  37. 37.Is 115465 divisible by 30?
  38. 38.Is 13770 divisible by 17?
  39. 39.Is 37253 divisible by 11?
  40. 40.Is 8264 divisible by 8?

Answer key

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

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