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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 379 · 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 19913 divisible by 4?
  2. 2.Is 31584 divisible by 24?
  3. 3.Is 4795 divisible by 2?
  4. 4.Is 2334 divisible by 6?
  5. 5.Is 69502 divisible by 30?
  6. 6.Is 46848 divisible by 24?
  7. 7.Is 180699 divisible by 29?
  8. 8.Is 31776 divisible by 9?
  9. 9.Is 48377 divisible by 9?
  10. 10.Is 105519 divisible by 29?
  11. 11.Is 35665 divisible by 7?
  12. 12.Is 29448 divisible by 6?
  13. 13.Is 11825 divisible by 13?
  14. 14.Is 40946 divisible by 10?
  15. 15.Is 21460 divisible by 4?
  16. 16.Is 31776 divisible by 17?
  17. 17.Is 53937 divisible by 11?
  18. 18.Is 50843 divisible by 13?
  19. 19.Is 53735 divisible by 30?
  20. 20.Is 20187 divisible by 7?
  21. 21.Is 126860 divisible by 20?
  22. 22.Is 27466 divisible by 4?
  23. 23.Is 56006 divisible by 18?
  24. 24.Is 16884 divisible by 29?
  25. 25.Is 70563 divisible by 15?
  26. 26.Is 73037 divisible by 17?
  27. 27.Is 38551 divisible by 11?
  28. 28.Is 15301 divisible by 7?
  29. 29.Is 44346 divisible by 10?
  30. 30.Is 78660 divisible by 19?
  31. 31.Is 13786 divisible by 2?
  32. 32.Is 10281 divisible by 6?
  33. 33.Is 9276 divisible by 3?
  34. 34.Is 29950 divisible by 5?
  35. 35.Is 30670 divisible by 12?
  36. 36.Is 53274 divisible by 13?
  37. 37.Is 11745 divisible by 29?
  38. 38.Is 22264 divisible by 23?
  39. 39.Is 89156 divisible by 13?
  40. 40.Is 73770 divisible by 30?

Answer key

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

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