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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 591 · 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 3030 divisible by 10?
  2. 2.Is 15644 divisible by 3?
  3. 3.Is 26354 divisible by 4?
  4. 4.Is 16944 divisible by 5?
  5. 5.Is 36941 divisible by 9?
  6. 6.Is 93843 divisible by 18?
  7. 7.Is 120648 divisible by 24?
  8. 8.Is 22232 divisible by 7?
  9. 9.Is 41179 divisible by 20?
  10. 10.Is 6591 divisible by 2?
  11. 11.Is 90740 divisible by 13?
  12. 12.Is 58531 divisible by 11?
  13. 13.Is 14767 divisible by 17?
  14. 14.Is 63864 divisible by 18?
  15. 15.Is 8788 divisible by 13?
  16. 16.Is 53370 divisible by 30?
  17. 17.Is 12405 divisible by 15?
  18. 18.Is 36301 divisible by 6?
  19. 19.Is 5118 divisible by 4?
  20. 20.Is 13445 divisible by 5?
  21. 21.Is 121762 divisible by 23?
  22. 22.Is 138651 divisible by 30?
  23. 23.Is 76705 divisible by 29?
  24. 24.Is 8482 divisible by 3?
  25. 25.Is 115926 divisible by 29?
  26. 26.Is 26012 divisible by 10?
  27. 27.Is 17642 divisible by 4?
  28. 28.Is 116991 divisible by 18?
  29. 29.Is 43479 divisible by 9?
  30. 30.Is 17231 divisible by 3?
  31. 31.Is 29230 divisible by 5?
  32. 32.Is 12219 divisible by 15?
  33. 33.Is 48420 divisible by 9?
  34. 34.Is 48076 divisible by 7?
  35. 35.Is 12959 divisible by 2?
  36. 36.Is 22304 divisible by 8?
  37. 37.Is 71435 divisible by 24?
  38. 38.Is 86961 divisible by 18?
  39. 39.Is 116798 divisible by 19?
  40. 40.Is 26181 divisible by 9?

Answer key

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

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