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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 128 · 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 41207 divisible by 10?
  2. 2.Is 36219 divisible by 19?
  3. 3.Is 22496 divisible by 4?
  4. 4.Is 35173 divisible by 13?
  5. 5.Is 23120 divisible by 8?
  6. 6.Is 48880 divisible by 20?
  7. 7.Is 62112 divisible by 12?
  8. 8.Is 177799 divisible by 29?
  9. 9.Is 99294 divisible by 19?
  10. 10.Is 26400 divisible by 4?
  11. 11.Is 88145 divisible by 17?
  12. 12.Is 17935 divisible by 23?
  13. 13.Is 118606 divisible by 18?
  14. 14.Is 12680 divisible by 5?
  15. 15.Is 82703 divisible by 12?
  16. 16.Is 7490 divisible by 10?
  17. 17.Is 35840 divisible by 6?
  18. 18.Is 19880 divisible by 5?
  19. 19.Is 14040 divisible by 8?
  20. 20.Is 22675 divisible by 6?
  21. 21.Is 20601 divisible by 7?
  22. 22.Is 28539 divisible by 12?
  23. 23.Is 22502 divisible by 18?
  24. 24.Is 97162 divisible by 23?
  25. 25.Is 8413 divisible by 3?
  26. 26.Is 185115 divisible by 30?
  27. 27.Is 134763 divisible by 29?
  28. 28.Is 6481 divisible by 3?
  29. 29.Is 40664 divisible by 20?
  30. 30.Is 172446 divisible by 29?
  31. 31.Is 6659 divisible by 7?
  32. 32.Is 13212 divisible by 4?
  33. 33.Is 110676 divisible by 23?
  34. 34.Is 18150 divisible by 15?
  35. 35.Is 40403 divisible by 6?
  36. 36.Is 147523 divisible by 29?
  37. 37.Is 153480 divisible by 24?
  38. 38.Is 88464 divisible by 24?
  39. 39.Is 8623 divisible by 2?
  40. 40.Is 57264 divisible by 19?

Answer key

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

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