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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 972 · 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 35103 divisible by 12?
  2. 2.Is 7777 divisible by 2?
  3. 3.Is 129912 divisible by 24?
  4. 4.Is 15071 divisible by 3?
  5. 5.Is 10683 divisible by 2?
  6. 6.Is 1608 divisible by 3?
  7. 7.Is 6918 divisible by 2?
  8. 8.Is 2275 divisible by 7?
  9. 9.Is 21811 divisible by 17?
  10. 10.Is 686 divisible by 18?
  11. 11.Is 5755 divisible by 2?
  12. 12.Is 3484 divisible by 3?
  13. 13.Is 29595 divisible by 5?
  14. 14.Is 26365 divisible by 6?
  15. 15.Is 51208 divisible by 8?
  16. 16.Is 170176 divisible by 29?
  17. 17.Is 21404 divisible by 4?
  18. 18.Is 25190 divisible by 5?
  19. 19.Is 32043 divisible by 17?
  20. 20.Is 99603 divisible by 18?
  21. 21.Is 45728 divisible by 8?
  22. 22.Is 68659 divisible by 23?
  23. 23.Is 7940 divisible by 2?
  24. 24.Is 37428 divisible by 6?
  25. 25.Is 13246 divisible by 2?
  26. 26.Is 56013 divisible by 13?
  27. 27.Is 73109 divisible by 11?
  28. 28.Is 47194 divisible by 7?
  29. 29.Is 9823 divisible by 17?
  30. 30.Is 88218 divisible by 18?
  31. 31.Is 7432 divisible by 4?
  32. 32.Is 26184 divisible by 11?
  33. 33.Is 12276 divisible by 4?
  34. 34.Is 29315 divisible by 5?
  35. 35.Is 42749 divisible by 7?
  36. 36.Is 52530 divisible by 30?
  37. 37.Is 6921 divisible by 9?
  38. 38.Is 70012 divisible by 15?
  39. 39.Is 5725 divisible by 5?
  40. 40.Is 12408 divisible by 2?

Answer key

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

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