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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 453 · 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 78180 divisible by 20?
  2. 2.Is 123827 divisible by 18?
  3. 3.Is 29410 divisible by 10?
  4. 4.Is 11294 divisible by 7?
  5. 5.Is 9408 divisible by 6?
  6. 6.Is 51813 divisible by 19?
  7. 7.Is 45430 divisible by 13?
  8. 8.Is 119935 divisible by 24?
  9. 9.Is 23450 divisible by 5?
  10. 10.Is 28388 divisible by 23?
  11. 11.Is 111552 divisible by 24?
  12. 12.Is 7088 divisible by 3?
  13. 13.Is 69433 divisible by 13?
  14. 14.Is 77452 divisible by 17?
  15. 15.Is 53972 divisible by 11?
  16. 16.Is 10357 divisible by 5?
  17. 17.Is 17315 divisible by 20?
  18. 18.Is 13383 divisible by 8?
  19. 19.Is 41581 divisible by 10?
  20. 20.Is 51339 divisible by 12?
  21. 21.Is 78965 divisible by 17?
  22. 22.Is 23536 divisible by 9?
  23. 23.Is 14238 divisible by 30?
  24. 24.Is 52954 divisible by 11?
  25. 25.Is 181308 divisible by 29?
  26. 26.Is 55818 divisible by 9?
  27. 27.Is 124837 divisible by 19?
  28. 28.Is 104272 divisible by 30?
  29. 29.Is 59622 divisible by 19?
  30. 30.Is 18376 divisible by 8?
  31. 31.Is 59657 divisible by 20?
  32. 32.Is 4776 divisible by 24?
  33. 33.Is 3807 divisible by 9?
  34. 34.Is 1924 divisible by 4?
  35. 35.Is 24406 divisible by 6?
  36. 36.Is 24905 divisible by 7?
  37. 37.Is 49174 divisible by 23?
  38. 38.Is 46577 divisible by 9?
  39. 39.Is 9948 divisible by 4?
  40. 40.Is 75986 divisible by 11?

Answer key

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

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