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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 712 · 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 9039 divisible by 4?
  2. 2.Is 4875 divisible by 2?
  3. 3.Is 52272 divisible by 18?
  4. 4.Is 21903 divisible by 7?
  5. 5.Is 202156 divisible by 30?
  6. 6.Is 10147 divisible by 11?
  7. 7.Is 7755 divisible by 2?
  8. 8.Is 6609 divisible by 2?
  9. 9.Is 44167 divisible by 7?
  10. 10.Is 156775 divisible by 24?
  11. 11.Is 70519 divisible by 12?
  12. 12.Is 7962 divisible by 3?
  13. 13.Is 16929 divisible by 6?
  14. 14.Is 13275 divisible by 3?
  15. 15.Is 40161 divisible by 11?
  16. 16.Is 138560 divisible by 20?
  17. 17.Is 23538 divisible by 13?
  18. 18.Is 31981 divisible by 8?
  19. 19.Is 8037 divisible by 2?
  20. 20.Is 76762 divisible by 11?
  21. 21.Is 20440 divisible by 10?
  22. 22.Is 18518 divisible by 11?
  23. 23.Is 4291 divisible by 7?
  24. 24.Is 1717 divisible by 2?
  25. 25.Is 53892 divisible by 18?
  26. 26.Is 9892 divisible by 4?
  27. 27.Is 15690 divisible by 8?
  28. 28.Is 11718 divisible by 19?
  29. 29.Is 98031 divisible by 30?
  30. 30.Is 36689 divisible by 19?
  31. 31.Is 10951 divisible by 2?
  32. 32.Is 117768 divisible by 24?
  33. 33.Is 3788 divisible by 3?
  34. 34.Is 24531 divisible by 6?
  35. 35.Is 112499 divisible by 19?
  36. 36.Is 31937 divisible by 19?
  37. 37.Is 29972 divisible by 5?
  38. 38.Is 40248 divisible by 8?
  39. 39.Is 3945 divisible by 2?
  40. 40.Is 41041 divisible by 13?

Answer key

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

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