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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 68 · 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 24699 divisible by 19?
  2. 2.Is 24263 divisible by 19?
  3. 3.Is 72516 divisible by 20?
  4. 4.Is 35829 divisible by 9?
  5. 5.Is 106585 divisible by 20?
  6. 6.Is 33320 divisible by 17?
  7. 7.Is 33950 divisible by 6?
  8. 8.Is 29570 divisible by 5?
  9. 9.Is 46060 divisible by 10?
  10. 10.Is 33507 divisible by 12?
  11. 11.Is 10555 divisible by 4?
  12. 12.Is 125970 divisible by 19?
  13. 13.Is 37369 divisible by 10?
  14. 14.Is 16211 divisible by 29?
  15. 15.Is 19313 divisible by 8?
  16. 16.Is 44270 divisible by 10?
  17. 17.Is 9464 divisible by 8?
  18. 18.Is 12075 divisible by 3?
  19. 19.Is 178901 divisible by 29?
  20. 20.Is 144657 divisible by 29?
  21. 21.Is 19456 divisible by 4?
  22. 22.Is 155846 divisible by 29?
  23. 23.Is 10355 divisible by 6?
  24. 24.Is 49882 divisible by 8?
  25. 25.Is 3171 divisible by 4?
  26. 26.Is 341 divisible by 2?
  27. 27.Is 124649 divisible by 20?
  28. 28.Is 7907 divisible by 18?
  29. 29.Is 72894 divisible by 17?
  30. 30.Is 23339 divisible by 13?
  31. 31.Is 21746 divisible by 4?
  32. 32.Is 21164 divisible by 4?
  33. 33.Is 9067 divisible by 3?
  34. 34.Is 2101 divisible by 11?
  35. 35.Is 46886 divisible by 18?
  36. 36.Is 9280 divisible by 10?
  37. 37.Is 8972 divisible by 2?
  38. 38.Is 135945 divisible by 24?
  39. 39.Is 4910 divisible by 2?
  40. 40.Is 39348 divisible by 9?

Answer key

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

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