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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 890 · 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 193437 divisible by 30?
  2. 2.Is 5520 divisible by 23?
  3. 3.Is 90720 divisible by 20?
  4. 4.Is 21316 divisible by 10?
  5. 5.Is 4524 divisible by 3?
  6. 6.Is 24844 divisible by 4?
  7. 7.Is 194833 divisible by 30?
  8. 8.Is 75976 divisible by 17?
  9. 9.Is 8864 divisible by 6?
  10. 10.Is 94743 divisible by 20?
  11. 11.Is 113716 divisible by 17?
  12. 12.Is 10842 divisible by 15?
  13. 13.Is 40980 divisible by 30?
  14. 14.Is 16116 divisible by 9?
  15. 15.Is 38114 divisible by 23?
  16. 16.Is 33560 divisible by 6?
  17. 17.Is 32443 divisible by 29?
  18. 18.Is 88380 divisible by 18?
  19. 19.Is 6584 divisible by 8?
  20. 20.Is 146970 divisible by 30?
  21. 21.Is 2673 divisible by 7?
  22. 22.Is 2920 divisible by 2?
  23. 23.Is 9249 divisible by 2?
  24. 24.Is 20417 divisible by 17?
  25. 25.Is 100532 divisible by 30?
  26. 26.Is 36408 divisible by 8?
  27. 27.Is 128508 divisible by 20?
  28. 28.Is 20520 divisible by 10?
  29. 29.Is 3916 divisible by 5?
  30. 30.Is 10493 divisible by 9?
  31. 31.Is 44840 divisible by 10?
  32. 32.Is 18102 divisible by 7?
  33. 33.Is 8032 divisible by 3?
  34. 34.Is 19149 divisible by 13?
  35. 35.Is 3019 divisible by 3?
  36. 36.Is 123004 divisible by 23?
  37. 37.Is 15840 divisible by 11?
  38. 38.Is 2836 divisible by 5?
  39. 39.Is 29525 divisible by 8?
  40. 40.Is 11755 divisible by 11?

Answer key

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

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