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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 699 · 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 460 divisible by 20?
  2. 2.Is 70311 divisible by 23?
  3. 3.Is 76590 divisible by 23?
  4. 4.Is 110494 divisible by 19?
  5. 5.Is 147338 divisible by 23?
  6. 6.Is 4283 divisible by 6?
  7. 7.Is 14757 divisible by 4?
  8. 8.Is 10449 divisible by 3?
  9. 9.Is 77731 divisible by 12?
  10. 10.Is 30618 divisible by 18?
  11. 11.Is 72888 divisible by 24?
  12. 12.Is 38204 divisible by 6?
  13. 13.Is 87860 divisible by 23?
  14. 14.Is 3681 divisible by 19?
  15. 15.Is 30363 divisible by 29?
  16. 16.Is 68520 divisible by 20?
  17. 17.Is 52755 divisible by 8?
  18. 18.Is 15784 divisible by 5?
  19. 19.Is 48699 divisible by 9?
  20. 20.Is 86505 divisible by 24?
  21. 21.Is 68497 divisible by 13?
  22. 22.Is 115296 divisible by 24?
  23. 23.Is 18864 divisible by 18?
  24. 24.Is 62737 divisible by 24?
  25. 25.Is 7376 divisible by 9?
  26. 26.Is 14186 divisible by 5?
  27. 27.Is 66246 divisible by 19?
  28. 28.Is 93252 divisible by 19?
  29. 29.Is 2408 divisible by 8?
  30. 30.Is 26327 divisible by 19?
  31. 31.Is 11502 divisible by 3?
  32. 32.Is 3111 divisible by 30?
  33. 33.Is 8761 divisible by 4?
  34. 34.Is 36856 divisible by 20?
  35. 35.Is 10278 divisible by 6?
  36. 36.Is 23860 divisible by 19?
  37. 37.Is 35290 divisible by 19?
  38. 38.Is 26937 divisible by 9?
  39. 39.Is 38649 divisible by 24?
  40. 40.Is 52470 divisible by 15?

Answer key

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

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