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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 152 · 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 74902 divisible by 11?
  2. 2.Is 32250 divisible by 30?
  3. 3.Is 13657 divisible by 2?
  4. 4.Is 58662 divisible by 9?
  5. 5.Is 103055 divisible by 20?
  6. 6.Is 87937 divisible by 15?
  7. 7.Is 11970 divisible by 5?
  8. 8.Is 20666 divisible by 8?
  9. 9.Is 22921 divisible by 13?
  10. 10.Is 98599 divisible by 15?
  11. 11.Is 85021 divisible by 17?
  12. 12.Is 72479 divisible by 11?
  13. 13.Is 33215 divisible by 18?
  14. 14.Is 41525 divisible by 20?
  15. 15.Is 9081 divisible by 4?
  16. 16.Is 20575 divisible by 17?
  17. 17.Is 29411 divisible by 6?
  18. 18.Is 108890 divisible by 18?
  19. 19.Is 13612 divisible by 2?
  20. 20.Is 70689 divisible by 15?
  21. 21.Is 75312 divisible by 13?
  22. 22.Is 336 divisible by 10?
  23. 23.Is 16577 divisible by 11?
  24. 24.Is 33745 divisible by 5?
  25. 25.Is 14065 divisible by 6?
  26. 26.Is 29052 divisible by 18?
  27. 27.Is 17478 divisible by 4?
  28. 28.Is 68712 divisible by 29?
  29. 29.Is 8415 divisible by 5?
  30. 30.Is 14973 divisible by 3?
  31. 31.Is 25586 divisible by 5?
  32. 32.Is 25360 divisible by 5?
  33. 33.Is 45043 divisible by 23?
  34. 34.Is 36615 divisible by 12?
  35. 35.Is 12925 divisible by 2?
  36. 36.Is 194382 divisible by 30?
  37. 37.Is 8208 divisible by 2?
  38. 38.Is 7952 divisible by 4?
  39. 39.Is 33654 divisible by 18?
  40. 40.Is 34421 divisible by 7?

Answer key

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

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