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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 452 · 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 11688 divisible by 24?
  2. 2.Is 20067 divisible by 3?
  3. 3.Is 87377 divisible by 29?
  4. 4.Is 110846 divisible by 19?
  5. 5.Is 7836 divisible by 6?
  6. 6.Is 32265 divisible by 7?
  7. 7.Is 25391 divisible by 7?
  8. 8.Is 5634 divisible by 2?
  9. 9.Is 29586 divisible by 6?
  10. 10.Is 18670 divisible by 10?
  11. 11.Is 38528 divisible by 8?
  12. 12.Is 43668 divisible by 9?
  13. 13.Is 112201 divisible by 24?
  14. 14.Is 124080 divisible by 30?
  15. 15.Is 1805 divisible by 3?
  16. 16.Is 42023 divisible by 10?
  17. 17.Is 24480 divisible by 5?
  18. 18.Is 8789 divisible by 4?
  19. 19.Is 53904 divisible by 24?
  20. 20.Is 15304 divisible by 3?
  21. 21.Is 90000 divisible by 15?
  22. 22.Is 7394 divisible by 9?
  23. 23.Is 98424 divisible by 18?
  24. 24.Is 13640 divisible by 20?
  25. 25.Is 166668 divisible by 24?
  26. 26.Is 35352 divisible by 12?
  27. 27.Is 15757 divisible by 7?
  28. 28.Is 19656 divisible by 18?
  29. 29.Is 29106 divisible by 5?
  30. 30.Is 22505 divisible by 19?
  31. 31.Is 23478 divisible by 9?
  32. 32.Is 645 divisible by 6?
  33. 33.Is 37687 divisible by 29?
  34. 34.Is 76077 divisible by 12?
  35. 35.Is 120118 divisible by 29?
  36. 36.Is 8710 divisible by 15?
  37. 37.Is 135644 divisible by 23?
  38. 38.Is 142536 divisible by 24?
  39. 39.Is 30018 divisible by 6?
  40. 40.Is 61879 divisible by 10?

Answer key

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

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