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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 30 · 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 8424 divisible by 13?
  2. 2.Is 17685 divisible by 23?
  3. 3.Is 121083 divisible by 19?
  4. 4.Is 32760 divisible by 9?
  5. 5.Is 15420 divisible by 3?
  6. 6.Is 30240 divisible by 20?
  7. 7.Is 1827 divisible by 7?
  8. 8.Is 1665 divisible by 6?
  9. 9.Is 36553 divisible by 30?
  10. 10.Is 15098 divisible by 5?
  11. 11.Is 51183 divisible by 8?
  12. 12.Is 254 divisible by 2?
  13. 13.Is 13972 divisible by 7?
  14. 14.Is 132480 divisible by 20?
  15. 15.Is 19481 divisible by 10?
  16. 16.Is 30578 divisible by 29?
  17. 17.Is 118184 divisible by 23?
  18. 18.Is 102574 divisible by 30?
  19. 19.Is 3041 divisible by 7?
  20. 20.Is 85104 divisible by 18?
  21. 21.Is 18408 divisible by 6?
  22. 22.Is 9161 divisible by 4?
  23. 23.Is 43020 divisible by 12?
  24. 24.Is 16448 divisible by 4?
  25. 25.Is 12838 divisible by 2?
  26. 26.Is 41024 divisible by 8?
  27. 27.Is 32099 divisible by 7?
  28. 28.Is 70521 divisible by 23?
  29. 29.Is 147472 divisible by 29?
  30. 30.Is 17320 divisible by 20?
  31. 31.Is 70720 divisible by 12?
  32. 32.Is 11834 divisible by 4?
  33. 33.Is 52253 divisible by 24?
  34. 34.Is 60986 divisible by 12?
  35. 35.Is 12421 divisible by 8?
  36. 36.Is 26947 divisible by 23?
  37. 37.Is 52770 divisible by 18?
  38. 38.Is 14756 divisible by 10?
  39. 39.Is 47043 divisible by 23?
  40. 40.Is 27748 divisible by 7?

Answer key

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

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