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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 943 · 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 65791 divisible by 11?
  2. 2.Is 20169 divisible by 4?
  3. 3.Is 3436 divisible by 3?
  4. 4.Is 30148 divisible by 19?
  5. 5.Is 13747 divisible by 2?
  6. 6.Is 29439 divisible by 9?
  7. 7.Is 4161 divisible by 2?
  8. 8.Is 27726 divisible by 6?
  9. 9.Is 55000 divisible by 13?
  10. 10.Is 47078 divisible by 7?
  11. 11.Is 3149 divisible by 15?
  12. 12.Is 67284 divisible by 29?
  13. 13.Is 31910 divisible by 5?
  14. 14.Is 43056 divisible by 8?
  15. 15.Is 11545 divisible by 7?
  16. 16.Is 34035 divisible by 30?
  17. 17.Is 200100 divisible by 29?
  18. 18.Is 42666 divisible by 12?
  19. 19.Is 56661 divisible by 10?
  20. 20.Is 5949 divisible by 9?
  21. 21.Is 12025 divisible by 9?
  22. 22.Is 44919 divisible by 23?
  23. 23.Is 19901 divisible by 6?
  24. 24.Is 1969 divisible by 2?
  25. 25.Is 42392 divisible by 10?
  26. 26.Is 58126 divisible by 18?
  27. 27.Is 10003 divisible by 7?
  28. 28.Is 168406 divisible by 29?
  29. 29.Is 98800 divisible by 23?
  30. 30.Is 7805 divisible by 4?
  31. 31.Is 89016 divisible by 18?
  32. 32.Is 80081 divisible by 19?
  33. 33.Is 152180 divisible by 24?
  34. 34.Is 12130 divisible by 3?
  35. 35.Is 29844 divisible by 6?
  36. 36.Is 1602 divisible by 6?
  37. 37.Is 9125 divisible by 2?
  38. 38.Is 123056 divisible by 18?
  39. 39.Is 44492 divisible by 7?
  40. 40.Is 14268 divisible by 4?

Answer key

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

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