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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 542 · 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 2573 divisible by 4?
  2. 2.Is 11379 divisible by 23?
  3. 3.Is 4127 divisible by 5?
  4. 4.Is 22143 divisible by 13?
  5. 5.Is 35961 divisible by 11?
  6. 6.Is 28794 divisible by 11?
  7. 7.Is 10180 divisible by 2?
  8. 8.Is 5842 divisible by 8?
  9. 9.Is 52150 divisible by 10?
  10. 10.Is 3904 divisible by 4?
  11. 11.Is 41769 divisible by 12?
  12. 12.Is 194886 divisible by 30?
  13. 13.Is 86386 divisible by 17?
  14. 14.Is 54559 divisible by 24?
  15. 15.Is 74985 divisible by 15?
  16. 16.Is 43703 divisible by 30?
  17. 17.Is 14496 divisible by 3?
  18. 18.Is 6942 divisible by 6?
  19. 19.Is 15347 divisible by 4?
  20. 20.Is 8716 divisible by 4?
  21. 21.Is 25284 divisible by 6?
  22. 22.Is 106513 divisible by 23?
  23. 23.Is 48712 divisible by 20?
  24. 24.Is 27703 divisible by 15?
  25. 25.Is 6793 divisible by 2?
  26. 26.Is 69048 divisible by 24?
  27. 27.Is 13561 divisible by 5?
  28. 28.Is 44620 divisible by 23?
  29. 29.Is 13424 divisible by 2?
  30. 30.Is 75072 divisible by 18?
  31. 31.Is 73043 divisible by 15?
  32. 32.Is 48615 divisible by 7?
  33. 33.Is 495 divisible by 10?
  34. 34.Is 88757 divisible by 17?
  35. 35.Is 33889 divisible by 12?
  36. 36.Is 32259 divisible by 6?
  37. 37.Is 16710 divisible by 10?
  38. 38.Is 39798 divisible by 18?
  39. 39.Is 28738 divisible by 17?
  40. 40.Is 109070 divisible by 17?

Answer key

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

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