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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 753 · 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 90828 divisible by 30?
  2. 2.Is 27885 divisible by 5?
  3. 3.Is 103169 divisible by 15?
  4. 4.Is 72529 divisible by 29?
  5. 5.Is 68718 divisible by 12?
  6. 6.Is 188819 divisible by 30?
  7. 7.Is 22562 divisible by 6?
  8. 8.Is 51800 divisible by 20?
  9. 9.Is 113408 divisible by 24?
  10. 10.Is 31057 divisible by 12?
  11. 11.Is 117534 divisible by 19?
  12. 12.Is 4736 divisible by 8?
  13. 13.Is 126746 divisible by 29?
  14. 14.Is 9090 divisible by 5?
  15. 15.Is 2142 divisible by 18?
  16. 16.Is 17761 divisible by 3?
  17. 17.Is 37633 divisible by 8?
  18. 18.Is 15439 divisible by 5?
  19. 19.Is 81000 divisible by 24?
  20. 20.Is 132112 divisible by 23?
  21. 21.Is 1145 divisible by 3?
  22. 22.Is 15805 divisible by 4?
  23. 23.Is 29907 divisible by 9?
  24. 24.Is 9649 divisible by 10?
  25. 25.Is 302 divisible by 4?
  26. 26.Is 98869 divisible by 15?
  27. 27.Is 12368 divisible by 6?
  28. 28.Is 15448 divisible by 4?
  29. 29.Is 10027 divisible by 11?
  30. 30.Is 29458 divisible by 13?
  31. 31.Is 132712 divisible by 20?
  32. 32.Is 4400 divisible by 30?
  33. 33.Is 35190 divisible by 17?
  34. 34.Is 61452 divisible by 12?
  35. 35.Is 52023 divisible by 12?
  36. 36.Is 93367 divisible by 17?
  37. 37.Is 33340 divisible by 5?
  38. 38.Is 33281 divisible by 5?
  39. 39.Is 171854 divisible by 29?
  40. 40.Is 57725 divisible by 13?

Answer key

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

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