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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 946 · 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 21856 divisible by 8?
  2. 2.Is 21312 divisible by 24?
  3. 3.Is 23493 divisible by 4?
  4. 4.Is 59364 divisible by 9?
  5. 5.Is 20399 divisible by 24?
  6. 6.Is 175102 divisible by 29?
  7. 7.Is 33950 divisible by 7?
  8. 8.Is 185659 divisible by 29?
  9. 9.Is 49344 divisible by 18?
  10. 10.Is 3951 divisible by 2?
  11. 11.Is 3508 divisible by 4?
  12. 12.Is 35808 divisible by 8?
  13. 13.Is 33345 divisible by 9?
  14. 14.Is 128656 divisible by 19?
  15. 15.Is 42205 divisible by 23?
  16. 16.Is 16858 divisible by 3?
  17. 17.Is 164952 divisible by 24?
  18. 18.Is 108571 divisible by 30?
  19. 19.Is 43946 divisible by 7?
  20. 20.Is 8965 divisible by 2?
  21. 21.Is 10887 divisible by 19?
  22. 22.Is 5564 divisible by 3?
  23. 23.Is 12254 divisible by 2?
  24. 24.Is 21536 divisible by 4?
  25. 25.Is 56563 divisible by 19?
  26. 26.Is 39243 divisible by 29?
  27. 27.Is 2776 divisible by 8?
  28. 28.Is 28552 divisible by 20?
  29. 29.Is 111740 divisible by 20?
  30. 30.Is 50146 divisible by 12?
  31. 31.Is 1030 divisible by 2?
  32. 32.Is 6127 divisible by 7?
  33. 33.Is 78071 divisible by 13?
  34. 34.Is 93704 divisible by 17?
  35. 35.Is 136416 divisible by 29?
  36. 36.Is 103364 divisible by 24?
  37. 37.Is 28488 divisible by 6?
  38. 38.Is 21945 divisible by 19?
  39. 39.Is 35255 divisible by 11?
  40. 40.Is 29891 divisible by 18?

Answer key

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

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