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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 745 · 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 29377 divisible by 29?
  2. 2.Is 426 divisible by 7?
  3. 3.Is 27931 divisible by 15?
  4. 4.Is 76431 divisible by 20?
  5. 5.Is 2622 divisible by 6?
  6. 6.Is 6789 divisible by 2?
  7. 7.Is 133240 divisible by 20?
  8. 8.Is 127900 divisible by 30?
  9. 9.Is 43928 divisible by 18?
  10. 10.Is 1521 divisible by 9?
  11. 11.Is 34361 divisible by 11?
  12. 12.Is 7461 divisible by 2?
  13. 13.Is 19343 divisible by 23?
  14. 14.Is 41232 divisible by 8?
  15. 15.Is 1468 divisible by 4?
  16. 16.Is 10111 divisible by 10?
  17. 17.Is 15032 divisible by 8?
  18. 18.Is 24647 divisible by 10?
  19. 19.Is 24575 divisible by 11?
  20. 20.Is 37588 divisible by 10?
  21. 21.Is 13266 divisible by 6?
  22. 22.Is 111389 divisible by 29?
  23. 23.Is 26571 divisible by 4?
  24. 24.Is 42792 divisible by 12?
  25. 25.Is 55262 divisible by 19?
  26. 26.Is 34862 divisible by 23?
  27. 27.Is 4380 divisible by 6?
  28. 28.Is 74424 divisible by 12?
  29. 29.Is 10295 divisible by 6?
  30. 30.Is 13421 divisible by 6?
  31. 31.Is 24536 divisible by 8?
  32. 32.Is 2184 divisible by 10?
  33. 33.Is 25272 divisible by 4?
  34. 34.Is 29602 divisible by 5?
  35. 35.Is 133142 divisible by 30?
  36. 36.Is 68392 divisible by 12?
  37. 37.Is 49904 divisible by 11?
  38. 38.Is 33670 divisible by 13?
  39. 39.Is 372 divisible by 2?
  40. 40.Is 53020 divisible by 10?

Answer key

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

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