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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 304 · 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 59323 divisible by 17?
  2. 2.Is 52273 divisible by 13?
  3. 3.Is 55818 divisible by 9?
  4. 4.Is 10451 divisible by 24?
  5. 5.Is 25513 divisible by 12?
  6. 6.Is 5770 divisible by 8?
  7. 7.Is 20385 divisible by 19?
  8. 8.Is 113952 divisible by 29?
  9. 9.Is 48289 divisible by 29?
  10. 10.Is 23173 divisible by 4?
  11. 11.Is 98979 divisible by 15?
  12. 12.Is 11134 divisible by 3?
  13. 13.Is 33336 divisible by 9?
  14. 14.Is 64325 divisible by 12?
  15. 15.Is 43229 divisible by 19?
  16. 16.Is 34041 divisible by 9?
  17. 17.Is 17064 divisible by 12?
  18. 18.Is 47425 divisible by 9?
  19. 19.Is 134404 divisible by 20?
  20. 20.Is 78749 divisible by 17?
  21. 21.Is 15961 divisible by 8?
  22. 22.Is 26689 divisible by 4?
  23. 23.Is 8428 divisible by 3?
  24. 24.Is 17817 divisible by 7?
  25. 25.Is 148656 divisible by 24?
  26. 26.Is 50934 divisible by 15?
  27. 27.Is 28985 divisible by 5?
  28. 28.Is 34682 divisible by 15?
  29. 29.Is 40849 divisible by 7?
  30. 30.Is 19006 divisible by 17?
  31. 31.Is 102940 divisible by 24?
  32. 32.Is 40612 divisible by 11?
  33. 33.Is 47169 divisible by 8?
  34. 34.Is 19359 divisible by 5?
  35. 35.Is 60036 divisible by 12?
  36. 36.Is 14163 divisible by 3?
  37. 37.Is 5944 divisible by 4?
  38. 38.Is 71010 divisible by 15?
  39. 39.Is 144170 divisible by 24?
  40. 40.Is 37630 divisible by 10?

Answer key

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

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