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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 297 · 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 67831 divisible by 29?
  2. 2.Is 13851 divisible by 9?
  3. 3.Is 18550 divisible by 7?
  4. 4.Is 11142 divisible by 2?
  5. 5.Is 5388 divisible by 11?
  6. 6.Is 101983 divisible by 19?
  7. 7.Is 145157 divisible by 23?
  8. 8.Is 55710 divisible by 10?
  9. 9.Is 34806 divisible by 6?
  10. 10.Is 2733 divisible by 9?
  11. 11.Is 42703 divisible by 7?
  12. 12.Is 28856 divisible by 8?
  13. 13.Is 1401 divisible by 7?
  14. 14.Is 32713 divisible by 19?
  15. 15.Is 132227 divisible by 23?
  16. 16.Is 25551 divisible by 6?
  17. 17.Is 158516 divisible by 23?
  18. 18.Is 36616 divisible by 29?
  19. 19.Is 3372 divisible by 6?
  20. 20.Is 8803 divisible by 2?
  21. 21.Is 27560 divisible by 4?
  22. 22.Is 6604 divisible by 4?
  23. 23.Is 12127 divisible by 2?
  24. 24.Is 71291 divisible by 11?
  25. 25.Is 21353 divisible by 6?
  26. 26.Is 9223 divisible by 4?
  27. 27.Is 19669 divisible by 17?
  28. 28.Is 32384 divisible by 11?
  29. 29.Is 22705 divisible by 12?
  30. 30.Is 110454 divisible by 19?
  31. 31.Is 17700 divisible by 20?
  32. 32.Is 165464 divisible by 30?
  33. 33.Is 156 divisible by 4?
  34. 34.Is 6348 divisible by 9?
  35. 35.Is 57240 divisible by 24?
  36. 36.Is 133900 divisible by 29?
  37. 37.Is 85310 divisible by 19?
  38. 38.Is 37301 divisible by 6?
  39. 39.Is 127259 divisible by 23?
  40. 40.Is 9240 divisible by 2?

Answer key

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

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