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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 882 · 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 72720 divisible by 30?
  2. 2.Is 152701 divisible by 30?
  3. 3.Is 137781 divisible by 20?
  4. 4.Is 101969 divisible by 30?
  5. 5.Is 164099 divisible by 30?
  6. 6.Is 12529 divisible by 30?
  7. 7.Is 92712 divisible by 23?
  8. 8.Is 24582 divisible by 6?
  9. 9.Is 106506 divisible by 18?
  10. 10.Is 34389 divisible by 20?
  11. 11.Is 58355 divisible by 23?
  12. 12.Is 34720 divisible by 7?
  13. 13.Is 43350 divisible by 17?
  14. 14.Is 113790 divisible by 30?
  15. 15.Is 33300 divisible by 18?
  16. 16.Is 40986 divisible by 6?
  17. 17.Is 10488 divisible by 8?
  18. 18.Is 33495 divisible by 20?
  19. 19.Is 42936 divisible by 24?
  20. 20.Is 12342 divisible by 6?
  21. 21.Is 43208 divisible by 11?
  22. 22.Is 11400 divisible by 24?
  23. 23.Is 32118 divisible by 6?
  24. 24.Is 3712 divisible by 8?
  25. 25.Is 32103 divisible by 9?
  26. 26.Is 14665 divisible by 7?
  27. 27.Is 20128 divisible by 8?
  28. 28.Is 24453 divisible by 11?
  29. 29.Is 101640 divisible by 20?
  30. 30.Is 8436 divisible by 7?
  31. 31.Is 18360 divisible by 24?
  32. 32.Is 156426 divisible by 29?
  33. 33.Is 55361 divisible by 29?
  34. 34.Is 20512 divisible by 4?
  35. 35.Is 72622 divisible by 20?
  36. 36.Is 54610 divisible by 9?
  37. 37.Is 41483 divisible by 12?
  38. 38.Is 10647 divisible by 4?
  39. 39.Is 35892 divisible by 6?
  40. 40.Is 51504 divisible by 29?

Answer key

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

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