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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 202 · 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 39435 divisible by 15?
  2. 2.Is 12816 divisible by 3?
  3. 3.Is 17694 divisible by 18?
  4. 4.Is 25660 divisible by 10?
  5. 5.Is 23827 divisible by 29?
  6. 6.Is 87333 divisible by 20?
  7. 7.Is 56540 divisible by 10?
  8. 8.Is 40976 divisible by 8?
  9. 9.Is 5264 divisible by 3?
  10. 10.Is 160609 divisible by 23?
  11. 11.Is 17514 divisible by 6?
  12. 12.Is 78140 divisible by 20?
  13. 13.Is 2690 divisible by 15?
  14. 14.Is 4470 divisible by 30?
  15. 15.Is 8064 divisible by 4?
  16. 16.Is 14814 divisible by 9?
  17. 17.Is 21177 divisible by 19?
  18. 18.Is 14200 divisible by 5?
  19. 19.Is 8979 divisible by 2?
  20. 20.Is 47411 divisible by 23?
  21. 21.Is 145782 divisible by 23?
  22. 22.Is 118436 divisible by 29?
  23. 23.Is 69089 divisible by 15?
  24. 24.Is 25820 divisible by 5?
  25. 25.Is 8157 divisible by 5?
  26. 26.Is 82547 divisible by 12?
  27. 27.Is 4576 divisible by 11?
  28. 28.Is 38527 divisible by 24?
  29. 29.Is 113832 divisible by 18?
  30. 30.Is 3886 divisible by 29?
  31. 31.Is 39721 divisible by 23?
  32. 32.Is 4044 divisible by 2?
  33. 33.Is 73367 divisible by 29?
  34. 34.Is 58719 divisible by 10?
  35. 35.Is 145020 divisible by 30?
  36. 36.Is 2631 divisible by 2?
  37. 37.Is 24456 divisible by 8?
  38. 38.Is 47768 divisible by 11?
  39. 39.Is 157054 divisible by 30?
  40. 40.Is 41790 divisible by 7?

Answer key

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

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