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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 294 · 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 25270 divisible by 10?
  2. 2.Is 2646 divisible by 9?
  3. 3.Is 6980 divisible by 5?
  4. 4.Is 21471 divisible by 6?
  5. 5.Is 28678 divisible by 30?
  6. 6.Is 130848 divisible by 24?
  7. 7.Is 25436 divisible by 24?
  8. 8.Is 61621 divisible by 15?
  9. 9.Is 7344 divisible by 18?
  10. 10.Is 105912 divisible by 24?
  11. 11.Is 6882 divisible by 2?
  12. 12.Is 3916 divisible by 4?
  13. 13.Is 19929 divisible by 8?
  14. 14.Is 3772 divisible by 2?
  15. 15.Is 7858 divisible by 3?
  16. 16.Is 6585 divisible by 2?
  17. 17.Is 30980 divisible by 13?
  18. 18.Is 53168 divisible by 8?
  19. 19.Is 152703 divisible by 23?
  20. 20.Is 51632 divisible by 30?
  21. 21.Is 52384 divisible by 17?
  22. 22.Is 56120 divisible by 20?
  23. 23.Is 31512 divisible by 5?
  24. 24.Is 55150 divisible by 10?
  25. 25.Is 26852 divisible by 11?
  26. 26.Is 13464 divisible by 5?
  27. 27.Is 6581 divisible by 2?
  28. 28.Is 4266 divisible by 3?
  29. 29.Is 113112 divisible by 24?
  30. 30.Is 2179 divisible by 2?
  31. 31.Is 9282 divisible by 6?
  32. 32.Is 27541 divisible by 8?
  33. 33.Is 10213 divisible by 7?
  34. 34.Is 34272 divisible by 17?
  35. 35.Is 12508 divisible by 19?
  36. 36.Is 8304 divisible by 4?
  37. 37.Is 16717 divisible by 7?
  38. 38.Is 53808 divisible by 8?
  39. 39.Is 897 divisible by 2?
  40. 40.Is 57304 divisible by 29?

Answer key

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

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