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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 754 · 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 10144 divisible by 4?
  2. 2.Is 25260 divisible by 15?
  3. 3.Is 20614 divisible by 7?
  4. 4.Is 50116 divisible by 10?
  5. 5.Is 13824 divisible by 6?
  6. 6.Is 5915 divisible by 9?
  7. 7.Is 47047 divisible by 7?
  8. 8.Is 116688 divisible by 17?
  9. 9.Is 21276 divisible by 13?
  10. 10.Is 120479 divisible by 19?
  11. 11.Is 29638 divisible by 8?
  12. 12.Is 15300 divisible by 20?
  13. 13.Is 12066 divisible by 5?
  14. 14.Is 47829 divisible by 17?
  15. 15.Is 2573 divisible by 7?
  16. 16.Is 33258 divisible by 5?
  17. 17.Is 30675 divisible by 9?
  18. 18.Is 785 divisible by 4?
  19. 19.Is 31220 divisible by 7?
  20. 20.Is 26886 divisible by 6?
  21. 21.Is 98751 divisible by 18?
  22. 22.Is 31746 divisible by 8?
  23. 23.Is 38831 divisible by 9?
  24. 24.Is 17245 divisible by 5?
  25. 25.Is 65105 divisible by 11?
  26. 26.Is 116318 divisible by 19?
  27. 27.Is 59660 divisible by 20?
  28. 28.Is 47801 divisible by 11?
  29. 29.Is 23516 divisible by 12?
  30. 30.Is 15118 divisible by 8?
  31. 31.Is 54002 divisible by 18?
  32. 32.Is 21052 divisible by 19?
  33. 33.Is 11875 divisible by 4?
  34. 34.Is 13295 divisible by 5?
  35. 35.Is 50347 divisible by 11?
  36. 36.Is 26560 divisible by 8?
  37. 37.Is 20561 divisible by 10?
  38. 38.Is 6858 divisible by 7?
  39. 39.Is 19905 divisible by 24?
  40. 40.Is 156483 divisible by 24?

Answer key

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

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