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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 489 · 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 46410 divisible by 13?
  2. 2.Is 55594 divisible by 10?
  3. 3.Is 14318 divisible by 17?
  4. 4.Is 13052 divisible by 8?
  5. 5.Is 65887 divisible by 11?
  6. 6.Is 60219 divisible by 9?
  7. 7.Is 16340 divisible by 6?
  8. 8.Is 71499 divisible by 17?
  9. 9.Is 191948 divisible by 29?
  10. 10.Is 55719 divisible by 10?
  11. 11.Is 2632 divisible by 2?
  12. 12.Is 15640 divisible by 24?
  13. 13.Is 16211 divisible by 4?
  14. 14.Is 20097 divisible by 11?
  15. 15.Is 21405 divisible by 15?
  16. 16.Is 42047 divisible by 19?
  17. 17.Is 132214 divisible by 20?
  18. 18.Is 49128 divisible by 24?
  19. 19.Is 53850 divisible by 10?
  20. 20.Is 10983 divisible by 2?
  21. 21.Is 32676 divisible by 6?
  22. 22.Is 9522 divisible by 3?
  23. 23.Is 18649 divisible by 7?
  24. 24.Is 9893 divisible by 5?
  25. 25.Is 8162 divisible by 29?
  26. 26.Is 31809 divisible by 5?
  27. 27.Is 11114 divisible by 4?
  28. 28.Is 15687 divisible by 7?
  29. 29.Is 9551 divisible by 4?
  30. 30.Is 6042 divisible by 5?
  31. 31.Is 10070 divisible by 19?
  32. 32.Is 74547 divisible by 11?
  33. 33.Is 11168 divisible by 2?
  34. 34.Is 9854 divisible by 6?
  35. 35.Is 3045 divisible by 12?
  36. 36.Is 23501 divisible by 7?
  37. 37.Is 16583 divisible by 23?
  38. 38.Is 16290 divisible by 7?
  39. 39.Is 108850 divisible by 24?
  40. 40.Is 32662 divisible by 6?

Answer key

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

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