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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 819 · 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 23751 divisible by 10?
  2. 2.Is 46777 divisible by 9?
  3. 3.Is 36460 divisible by 7?
  4. 4.Is 66599 divisible by 13?
  5. 5.Is 11496 divisible by 7?
  6. 6.Is 39883 divisible by 18?
  7. 7.Is 34830 divisible by 5?
  8. 8.Is 20010 divisible by 6?
  9. 9.Is 13508 divisible by 3?
  10. 10.Is 28595 divisible by 7?
  11. 11.Is 30475 divisible by 23?
  12. 12.Is 4224 divisible by 8?
  13. 13.Is 92070 divisible by 18?
  14. 14.Is 142608 divisible by 24?
  15. 15.Is 145377 divisible by 29?
  16. 16.Is 52764 divisible by 9?
  17. 17.Is 634 divisible by 3?
  18. 18.Is 1488 divisible by 2?
  19. 19.Is 18821 divisible by 11?
  20. 20.Is 125524 divisible by 23?
  21. 21.Is 60498 divisible by 18?
  22. 22.Is 1049 divisible by 11?
  23. 23.Is 33901 divisible by 29?
  24. 24.Is 65220 divisible by 19?
  25. 25.Is 70511 divisible by 17?
  26. 26.Is 4918 divisible by 24?
  27. 27.Is 63523 divisible by 10?
  28. 28.Is 9783 divisible by 3?
  29. 29.Is 20898 divisible by 3?
  30. 30.Is 36932 divisible by 7?
  31. 31.Is 34960 divisible by 8?
  32. 32.Is 129835 divisible by 23?
  33. 33.Is 61537 divisible by 9?
  34. 34.Is 24948 divisible by 9?
  35. 35.Is 117943 divisible by 29?
  36. 36.Is 38917 divisible by 8?
  37. 37.Is 112140 divisible by 18?
  38. 38.Is 34560 divisible by 20?
  39. 39.Is 5969 divisible by 29?
  40. 40.Is 61290 divisible by 30?

Answer key

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

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