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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 337 · 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 81737 divisible by 15?
  2. 2.Is 4450 divisible by 10?
  3. 3.Is 16350 divisible by 5?
  4. 4.Is 61936 divisible by 10?
  5. 5.Is 35959 divisible by 7?
  6. 6.Is 96222 divisible by 29?
  7. 7.Is 2235 divisible by 15?
  8. 8.Is 117079 divisible by 19?
  9. 9.Is 32436 divisible by 9?
  10. 10.Is 30100 divisible by 7?
  11. 11.Is 6166 divisible by 3?
  12. 12.Is 56131 divisible by 15?
  13. 13.Is 77340 divisible by 12?
  14. 14.Is 24616 divisible by 5?
  15. 15.Is 5103 divisible by 3?
  16. 16.Is 62397 divisible by 13?
  17. 17.Is 121014 divisible by 18?
  18. 18.Is 47993 divisible by 18?
  19. 19.Is 23769 divisible by 9?
  20. 20.Is 118820 divisible by 20?
  21. 21.Is 135600 divisible by 30?
  22. 22.Is 29610 divisible by 18?
  23. 23.Is 9225 divisible by 3?
  24. 24.Is 27829 divisible by 6?
  25. 25.Is 30059 divisible by 20?
  26. 26.Is 8296 divisible by 4?
  27. 27.Is 48314 divisible by 7?
  28. 28.Is 39559 divisible by 13?
  29. 29.Is 3724 divisible by 2?
  30. 30.Is 91780 divisible by 20?
  31. 31.Is 24319 divisible by 4?
  32. 32.Is 62100 divisible by 15?
  33. 33.Is 16994 divisible by 4?
  34. 34.Is 1561 divisible by 5?
  35. 35.Is 29780 divisible by 10?
  36. 36.Is 49401 divisible by 11?
  37. 37.Is 65956 divisible by 11?
  38. 38.Is 147 divisible by 6?
  39. 39.Is 2640 divisible by 15?
  40. 40.Is 110732 divisible by 19?

Answer key

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

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