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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 821 · 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 58464 divisible by 10?
  2. 2.Is 895 divisible by 3?
  3. 3.Is 6024 divisible by 6?
  4. 4.Is 75052 divisible by 29?
  5. 5.Is 7980 divisible by 20?
  6. 6.Is 5685 divisible by 2?
  7. 7.Is 20241 divisible by 3?
  8. 8.Is 23218 divisible by 19?
  9. 9.Is 20709 divisible by 5?
  10. 10.Is 6000 divisible by 24?
  11. 11.Is 80861 divisible by 29?
  12. 12.Is 14840 divisible by 10?
  13. 13.Is 271 divisible by 2?
  14. 14.Is 49730 divisible by 20?
  15. 15.Is 177118 divisible by 30?
  16. 16.Is 82412 divisible by 12?
  17. 17.Is 55828 divisible by 19?
  18. 18.Is 57048 divisible by 24?
  19. 19.Is 46229 divisible by 20?
  20. 20.Is 1740 divisible by 2?
  21. 21.Is 17036 divisible by 11?
  22. 22.Is 1771 divisible by 3?
  23. 23.Is 16385 divisible by 3?
  24. 24.Is 98175 divisible by 18?
  25. 25.Is 48215 divisible by 19?
  26. 26.Is 30499 divisible by 8?
  27. 27.Is 4865 divisible by 3?
  28. 28.Is 133883 divisible by 23?
  29. 29.Is 38076 divisible by 12?
  30. 30.Is 98363 divisible by 18?
  31. 31.Is 28547 divisible by 12?
  32. 32.Is 68172 divisible by 19?
  33. 33.Is 33552 divisible by 24?
  34. 34.Is 682 divisible by 7?
  35. 35.Is 89670 divisible by 15?
  36. 36.Is 25272 divisible by 12?
  37. 37.Is 35574 divisible by 11?
  38. 38.Is 124589 divisible by 24?
  39. 39.Is 1256 divisible by 4?
  40. 40.Is 20311 divisible by 9?

Answer key

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

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