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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 40 · 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 38052 divisible by 7?
  2. 2.Is 81806 divisible by 13?
  3. 3.Is 3060 divisible by 18?
  4. 4.Is 67105 divisible by 18?
  5. 5.Is 79659 divisible by 18?
  6. 6.Is 11710 divisible by 2?
  7. 7.Is 5568 divisible by 29?
  8. 8.Is 17460 divisible by 3?
  9. 9.Is 95760 divisible by 18?
  10. 10.Is 7937 divisible by 3?
  11. 11.Is 76590 divisible by 12?
  12. 12.Is 15850 divisible by 6?
  13. 13.Is 29229 divisible by 8?
  14. 14.Is 86014 divisible by 23?
  15. 15.Is 17777 divisible by 12?
  16. 16.Is 163656 divisible by 24?
  17. 17.Is 31032 divisible by 6?
  18. 18.Is 10970 divisible by 2?
  19. 19.Is 13782 divisible by 23?
  20. 20.Is 34535 divisible by 5?
  21. 21.Is 13638 divisible by 6?
  22. 22.Is 27785 divisible by 6?
  23. 23.Is 49374 divisible by 9?
  24. 24.Is 11148 divisible by 23?
  25. 25.Is 19608 divisible by 19?
  26. 26.Is 1866 divisible by 2?
  27. 27.Is 26154 divisible by 6?
  28. 28.Is 4310 divisible by 10?
  29. 29.Is 39553 divisible by 17?
  30. 30.Is 53162 divisible by 29?
  31. 31.Is 28328 divisible by 8?
  32. 32.Is 854 divisible by 11?
  33. 33.Is 37505 divisible by 6?
  34. 34.Is 194716 divisible by 30?
  35. 35.Is 24307 divisible by 6?
  36. 36.Is 96840 divisible by 18?
  37. 37.Is 24688 divisible by 4?
  38. 38.Is 1092 divisible by 13?
  39. 39.Is 59848 divisible by 23?
  40. 40.Is 15859 divisible by 9?

Answer key

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

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