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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 554 · 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 11313 divisible by 30?
  2. 2.Is 92700 divisible by 15?
  3. 3.Is 107841 divisible by 23?
  4. 4.Is 21400 divisible by 10?
  5. 5.Is 67015 divisible by 13?
  6. 6.Is 4543 divisible by 7?
  7. 7.Is 13551 divisible by 3?
  8. 8.Is 53528 divisible by 11?
  9. 9.Is 133710 divisible by 30?
  10. 10.Is 2736 divisible by 4?
  11. 11.Is 72600 divisible by 20?
  12. 12.Is 9156 divisible by 3?
  13. 13.Is 19047 divisible by 7?
  14. 14.Is 2831 divisible by 4?
  15. 15.Is 61848 divisible by 12?
  16. 16.Is 24720 divisible by 20?
  17. 17.Is 8195 divisible by 5?
  18. 18.Is 9310 divisible by 6?
  19. 19.Is 17464 divisible by 30?
  20. 20.Is 135409 divisible by 30?
  21. 21.Is 8553 divisible by 2?
  22. 22.Is 32004 divisible by 18?
  23. 23.Is 27083 divisible by 6?
  24. 24.Is 6005 divisible by 2?
  25. 25.Is 7368 divisible by 6?
  26. 26.Is 12694 divisible by 11?
  27. 27.Is 12495 divisible by 17?
  28. 28.Is 19420 divisible by 5?
  29. 29.Is 119115 divisible by 24?
  30. 30.Is 10953 divisible by 9?
  31. 31.Is 34341 divisible by 9?
  32. 32.Is 167700 divisible by 30?
  33. 33.Is 20020 divisible by 13?
  34. 34.Is 53520 divisible by 12?
  35. 35.Is 106224 divisible by 24?
  36. 36.Is 11175 divisible by 9?
  37. 37.Is 5684 divisible by 24?
  38. 38.Is 751 divisible by 2?
  39. 39.Is 56771 divisible by 11?
  40. 40.Is 26832 divisible by 13?

Answer key

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

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