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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 301 · 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 13746 divisible by 10?
  2. 2.Is 49482 divisible by 18?
  3. 3.Is 15528 divisible by 8?
  4. 4.Is 20800 divisible by 10?
  5. 5.Is 42266 divisible by 19?
  6. 6.Is 6240 divisible by 6?
  7. 7.Is 141491 divisible by 29?
  8. 8.Is 161559 divisible by 29?
  9. 9.Is 90957 divisible by 23?
  10. 10.Is 17672 divisible by 17?
  11. 11.Is 20490 divisible by 3?
  12. 12.Is 16527 divisible by 17?
  13. 13.Is 117486 divisible by 19?
  14. 14.Is 840 divisible by 30?
  15. 15.Is 24091 divisible by 4?
  16. 16.Is 14727 divisible by 13?
  17. 17.Is 113145 divisible by 19?
  18. 18.Is 60912 divisible by 12?
  19. 19.Is 54720 divisible by 8?
  20. 20.Is 3090 divisible by 30?
  21. 21.Is 2798 divisible by 3?
  22. 22.Is 76430 divisible by 18?
  23. 23.Is 38772 divisible by 8?
  24. 24.Is 77403 divisible by 12?
  25. 25.Is 6947 divisible by 24?
  26. 26.Is 50040 divisible by 9?
  27. 27.Is 51538 divisible by 10?
  28. 28.Is 65818 divisible by 17?
  29. 29.Is 121001 divisible by 23?
  30. 30.Is 14199 divisible by 3?
  31. 31.Is 29552 divisible by 8?
  32. 32.Is 47357 divisible by 23?
  33. 33.Is 120408 divisible by 29?
  34. 34.Is 14874 divisible by 8?
  35. 35.Is 43283 divisible by 10?
  36. 36.Is 41454 divisible by 18?
  37. 37.Is 9496 divisible by 4?
  38. 38.Is 10184 divisible by 4?
  39. 39.Is 4428 divisible by 6?
  40. 40.Is 147584 divisible by 24?

Answer key

  1. no
  2. yes
  3. yes
  4. yes
  5. no
  6. yes
  7. yes
  8. yes
  9. no
  10. no
  11. yes
  12. no
  13. no
  14. yes
  15. no
  16. no
  17. yes
  18. yes
  19. yes
  20. yes
  21. no
  22. no
  23. no
  24. no
  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. yes
  38. yes
  39. yes
  40. no

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