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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 430 · 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 14301 divisible by 20?
  2. 2.Is 42033 divisible by 8?
  3. 3.Is 31637 divisible by 5?
  4. 4.Is 11025 divisible by 7?
  5. 5.Is 73290 divisible by 30?
  6. 6.Is 43808 divisible by 10?
  7. 7.Is 76197 divisible by 11?
  8. 8.Is 10448 divisible by 8?
  9. 9.Is 6687 divisible by 9?
  10. 10.Is 80760 divisible by 20?
  11. 11.Is 1462 divisible by 3?
  12. 12.Is 103755 divisible by 15?
  13. 13.Is 29778 divisible by 6?
  14. 14.Is 91307 divisible by 17?
  15. 15.Is 38640 divisible by 24?
  16. 16.Is 1849 divisible by 7?
  17. 17.Is 10842 divisible by 6?
  18. 18.Is 35732 divisible by 6?
  19. 19.Is 6031 divisible by 9?
  20. 20.Is 4428 divisible by 3?
  21. 21.Is 31208 divisible by 9?
  22. 22.Is 14310 divisible by 30?
  23. 23.Is 34866 divisible by 13?
  24. 24.Is 73500 divisible by 20?
  25. 25.Is 88247 divisible by 29?
  26. 26.Is 724 divisible by 2?
  27. 27.Is 7933 divisible by 2?
  28. 28.Is 99524 divisible by 18?
  29. 29.Is 34040 divisible by 23?
  30. 30.Is 1744 divisible by 2?
  31. 31.Is 654 divisible by 18?
  32. 32.Is 79118 divisible by 13?
  33. 33.Is 112336 divisible by 17?
  34. 34.Is 3504 divisible by 2?
  35. 35.Is 5241 divisible by 3?
  36. 36.Is 44751 divisible by 7?
  37. 37.Is 21645 divisible by 4?
  38. 38.Is 31962 divisible by 10?
  39. 39.Is 44524 divisible by 9?
  40. 40.Is 37516 divisible by 13?

Answer key

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

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