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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 451 · 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 13884 divisible by 6?
  2. 2.Is 6825 divisible by 10?
  3. 3.Is 8690 divisible by 3?
  4. 4.Is 8233 divisible by 10?
  5. 5.Is 25890 divisible by 30?
  6. 6.Is 9303 divisible by 5?
  7. 7.Is 15480 divisible by 29?
  8. 8.Is 2401 divisible by 7?
  9. 9.Is 80290 divisible by 12?
  10. 10.Is 29077 divisible by 20?
  11. 11.Is 64275 divisible by 15?
  12. 12.Is 71190 divisible by 18?
  13. 13.Is 770 divisible by 5?
  14. 14.Is 975 divisible by 2?
  15. 15.Is 31009 divisible by 10?
  16. 16.Is 27671 divisible by 9?
  17. 17.Is 114837 divisible by 23?
  18. 18.Is 5571 divisible by 3?
  19. 19.Is 146137 divisible by 24?
  20. 20.Is 101526 divisible by 19?
  21. 21.Is 9371 divisible by 8?
  22. 22.Is 38592 divisible by 12?
  23. 23.Is 15279 divisible by 3?
  24. 24.Is 35001 divisible by 29?
  25. 25.Is 77596 divisible by 13?
  26. 26.Is 32807 divisible by 9?
  27. 27.Is 74565 divisible by 15?
  28. 28.Is 79115 divisible by 17?
  29. 29.Is 7526 divisible by 4?
  30. 30.Is 121882 divisible by 19?
  31. 31.Is 23781 divisible by 10?
  32. 32.Is 49431 divisible by 18?
  33. 33.Is 38360 divisible by 20?
  34. 34.Is 67860 divisible by 18?
  35. 35.Is 11342 divisible by 18?
  36. 36.Is 37554 divisible by 15?
  37. 37.Is 84430 divisible by 13?
  38. 38.Is 11418 divisible by 6?
  39. 39.Is 8173 divisible by 6?
  40. 40.Is 105831 divisible by 19?

Answer key

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

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