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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 394 · 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 12573 divisible by 3?
  2. 2.Is 58036 divisible by 29?
  3. 3.Is 18221 divisible by 6?
  4. 4.Is 49332 divisible by 20?
  5. 5.Is 14048 divisible by 15?
  6. 6.Is 5236 divisible by 11?
  7. 7.Is 35244 divisible by 10?
  8. 8.Is 38208 divisible by 24?
  9. 9.Is 18800 divisible by 8?
  10. 10.Is 7344 divisible by 2?
  11. 11.Is 9744 divisible by 7?
  12. 12.Is 380 divisible by 2?
  13. 13.Is 19560 divisible by 6?
  14. 14.Is 54094 divisible by 17?
  15. 15.Is 67280 divisible by 29?
  16. 16.Is 7011 divisible by 6?
  17. 17.Is 7956 divisible by 17?
  18. 18.Is 99603 divisible by 24?
  19. 19.Is 26940 divisible by 5?
  20. 20.Is 31880 divisible by 15?
  21. 21.Is 129795 divisible by 19?
  22. 22.Is 6470 divisible by 10?
  23. 23.Is 36093 divisible by 10?
  24. 24.Is 5461 divisible by 24?
  25. 25.Is 1442 divisible by 2?
  26. 26.Is 2073 divisible by 23?
  27. 27.Is 27900 divisible by 30?
  28. 28.Is 19860 divisible by 5?
  29. 29.Is 30927 divisible by 13?
  30. 30.Is 105220 divisible by 20?
  31. 31.Is 20775 divisible by 11?
  32. 32.Is 10644 divisible by 6?
  33. 33.Is 1590 divisible by 9?
  34. 34.Is 16848 divisible by 24?
  35. 35.Is 158164 divisible by 24?
  36. 36.Is 43048 divisible by 9?
  37. 37.Is 52284 divisible by 30?
  38. 38.Is 63134 divisible by 29?
  39. 39.Is 64342 divisible by 29?
  40. 40.Is 146234 divisible by 23?

Answer key

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

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