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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 599 · 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 20518 divisible by 5?
  2. 2.Is 62999 divisible by 11?
  3. 3.Is 52358 divisible by 19?
  4. 4.Is 20488 divisible by 4?
  5. 5.Is 2068 divisible by 4?
  6. 6.Is 28677 divisible by 20?
  7. 7.Is 147476 divisible by 23?
  8. 8.Is 13688 divisible by 4?
  9. 9.Is 25320 divisible by 6?
  10. 10.Is 54405 divisible by 13?
  11. 11.Is 10972 divisible by 5?
  12. 12.Is 28611 divisible by 8?
  13. 13.Is 41507 divisible by 10?
  14. 14.Is 9417 divisible by 5?
  15. 15.Is 38047 divisible by 9?
  16. 16.Is 63883 divisible by 23?
  17. 17.Is 2940 divisible by 10?
  18. 18.Is 13997 divisible by 4?
  19. 19.Is 13234 divisible by 2?
  20. 20.Is 42515 divisible by 24?
  21. 21.Is 122840 divisible by 20?
  22. 22.Is 72252 divisible by 18?
  23. 23.Is 68376 divisible by 12?
  24. 24.Is 15240 divisible by 4?
  25. 25.Is 2562 divisible by 3?
  26. 26.Is 4752 divisible by 6?
  27. 27.Is 165384 divisible by 24?
  28. 28.Is 35654 divisible by 30?
  29. 29.Is 109108 divisible by 30?
  30. 30.Is 6249 divisible by 6?
  31. 31.Is 25736 divisible by 4?
  32. 32.Is 24759 divisible by 9?
  33. 33.Is 1796 divisible by 4?
  34. 34.Is 5033 divisible by 7?
  35. 35.Is 119232 divisible by 18?
  36. 36.Is 45756 divisible by 18?
  37. 37.Is 26055 divisible by 4?
  38. 38.Is 38874 divisible by 20?
  39. 39.Is 65890 divisible by 10?
  40. 40.Is 97314 divisible by 17?

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. no
  13. no
  14. no
  15. no
  16. no
  17. yes
  18. no
  19. yes
  20. no
  21. yes
  22. yes
  23. yes
  24. yes
  25. yes
  26. yes
  27. yes
  28. no
  29. no
  30. no
  31. yes
  32. yes
  33. yes
  34. yes
  35. yes
  36. yes
  37. no
  38. no
  39. yes
  40. no

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