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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 861 · 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 9739 divisible by 5?
  2. 2.Is 43988 divisible by 7?
  3. 3.Is 45337 divisible by 7?
  4. 4.Is 10361 divisible by 2?
  5. 5.Is 14470 divisible by 9?
  6. 6.Is 1592 divisible by 5?
  7. 7.Is 18972 divisible by 12?
  8. 8.Is 75306 divisible by 11?
  9. 9.Is 6105 divisible by 3?
  10. 10.Is 1560 divisible by 15?
  11. 11.Is 277 divisible by 7?
  12. 12.Is 145290 divisible by 30?
  13. 13.Is 12464 divisible by 9?
  14. 14.Is 20612 divisible by 4?
  15. 15.Is 45585 divisible by 7?
  16. 16.Is 5541 divisible by 10?
  17. 17.Is 43645 divisible by 9?
  18. 18.Is 19701 divisible by 11?
  19. 19.Is 29595 divisible by 15?
  20. 20.Is 59851 divisible by 9?
  21. 21.Is 17130 divisible by 10?
  22. 22.Is 29857 divisible by 5?
  23. 23.Is 40426 divisible by 20?
  24. 24.Is 3010 divisible by 2?
  25. 25.Is 32410 divisible by 12?
  26. 26.Is 3997 divisible by 7?
  27. 27.Is 47804 divisible by 18?
  28. 28.Is 24056 divisible by 9?
  29. 29.Is 69578 divisible by 15?
  30. 30.Is 91480 divisible by 20?
  31. 31.Is 21641 divisible by 19?
  32. 32.Is 3364 divisible by 2?
  33. 33.Is 18000 divisible by 10?
  34. 34.Is 15344 divisible by 30?
  35. 35.Is 46429 divisible by 9?
  36. 36.Is 78840 divisible by 12?
  37. 37.Is 6121 divisible by 24?
  38. 38.Is 44916 divisible by 12?
  39. 39.Is 40224 divisible by 6?
  40. 40.Is 10136 divisible by 3?

Answer key

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

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