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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 572 · 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 2175 divisible by 3?
  2. 2.Is 122382 divisible by 18?
  3. 3.Is 11305 divisible by 3?
  4. 4.Is 28532 divisible by 18?
  5. 5.Is 8670 divisible by 5?
  6. 6.Is 33216 divisible by 12?
  7. 7.Is 77178 divisible by 19?
  8. 8.Is 14070 divisible by 5?
  9. 9.Is 137460 divisible by 29?
  10. 10.Is 4267 divisible by 2?
  11. 11.Is 75570 divisible by 30?
  12. 12.Is 48489 divisible by 7?
  13. 13.Is 27390 divisible by 4?
  14. 14.Is 46830 divisible by 30?
  15. 15.Is 19131 divisible by 3?
  16. 16.Is 17560 divisible by 8?
  17. 17.Is 106822 divisible by 19?
  18. 18.Is 94583 divisible by 18?
  19. 19.Is 154466 divisible by 23?
  20. 20.Is 12342 divisible by 3?
  21. 21.Is 9460 divisible by 20?
  22. 22.Is 4908 divisible by 12?
  23. 23.Is 94824 divisible by 18?
  24. 24.Is 6507 divisible by 2?
  25. 25.Is 45530 divisible by 20?
  26. 26.Is 75480 divisible by 17?
  27. 27.Is 53719 divisible by 12?
  28. 28.Is 25006 divisible by 12?
  29. 29.Is 10850 divisible by 2?
  30. 30.Is 10525 divisible by 30?
  31. 31.Is 144891 divisible by 29?
  32. 32.Is 15309 divisible by 3?
  33. 33.Is 32606 divisible by 19?
  34. 34.Is 65956 divisible by 18?
  35. 35.Is 17461 divisible by 5?
  36. 36.Is 13503 divisible by 6?
  37. 37.Is 14340 divisible by 10?
  38. 38.Is 1755 divisible by 2?
  39. 39.Is 72244 divisible by 19?
  40. 40.Is 12361 divisible by 2?

Answer key

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

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