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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 719 · 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 31180 divisible by 5?
  2. 2.Is 42108 divisible by 12?
  3. 3.Is 8407 divisible by 5?
  4. 4.Is 38797 divisible by 19?
  5. 5.Is 50933 divisible by 13?
  6. 6.Is 47355 divisible by 11?
  7. 7.Is 18696 divisible by 19?
  8. 8.Is 59085 divisible by 15?
  9. 9.Is 38313 divisible by 8?
  10. 10.Is 22805 divisible by 5?
  11. 11.Is 61306 divisible by 17?
  12. 12.Is 44480 divisible by 10?
  13. 13.Is 50121 divisible by 9?
  14. 14.Is 28228 divisible by 8?
  15. 15.Is 28178 divisible by 11?
  16. 16.Is 69354 divisible by 18?
  17. 17.Is 7588 divisible by 2?
  18. 18.Is 6416 divisible by 9?
  19. 19.Is 38112 divisible by 6?
  20. 20.Is 12048 divisible by 6?
  21. 21.Is 9675 divisible by 9?
  22. 22.Is 21840 divisible by 30?
  23. 23.Is 18676 divisible by 3?
  24. 24.Is 2362 divisible by 3?
  25. 25.Is 17920 divisible by 3?
  26. 26.Is 17717 divisible by 6?
  27. 27.Is 10290 divisible by 6?
  28. 28.Is 32634 divisible by 8?
  29. 29.Is 195660 divisible by 30?
  30. 30.Is 2995 divisible by 15?
  31. 31.Is 56720 divisible by 20?
  32. 32.Is 31034 divisible by 5?
  33. 33.Is 92451 divisible by 29?
  34. 34.Is 6950 divisible by 12?
  35. 35.Is 26405 divisible by 7?
  36. 36.Is 3430 divisible by 3?
  37. 37.Is 54958 divisible by 10?
  38. 38.Is 12414 divisible by 15?
  39. 39.Is 9723 divisible by 5?
  40. 40.Is 113411 divisible by 24?

Answer key

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

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