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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 189 · 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 8603 divisible by 9?
  2. 2.Is 8491 divisible by 5?
  3. 3.Is 31621 divisible by 9?
  4. 4.Is 19608 divisible by 19?
  5. 5.Is 10440 divisible by 4?
  6. 6.Is 23970 divisible by 17?
  7. 7.Is 16670 divisible by 3?
  8. 8.Is 55971 divisible by 11?
  9. 9.Is 14931 divisible by 3?
  10. 10.Is 13432 divisible by 4?
  11. 11.Is 44581 divisible by 8?
  12. 12.Is 14394 divisible by 3?
  13. 13.Is 38755 divisible by 23?
  14. 14.Is 7263 divisible by 2?
  15. 15.Is 87116 divisible by 15?
  16. 16.Is 1708 divisible by 2?
  17. 17.Is 1031 divisible by 10?
  18. 18.Is 45172 divisible by 23?
  19. 19.Is 42432 divisible by 15?
  20. 20.Is 28170 divisible by 30?
  21. 21.Is 11480 divisible by 5?
  22. 22.Is 22943 divisible by 17?
  23. 23.Is 6436 divisible by 2?
  24. 24.Is 26296 divisible by 4?
  25. 25.Is 52768 divisible by 10?
  26. 26.Is 21917 divisible by 7?
  27. 27.Is 47376 divisible by 9?
  28. 28.Is 33236 divisible by 7?
  29. 29.Is 132832 divisible by 20?
  30. 30.Is 31599 divisible by 9?
  31. 31.Is 3538 divisible by 5?
  32. 32.Is 15255 divisible by 9?
  33. 33.Is 24228 divisible by 5?
  34. 34.Is 7928 divisible by 3?
  35. 35.Is 35037 divisible by 17?
  36. 36.Is 1366 divisible by 7?
  37. 37.Is 157826 divisible by 23?
  38. 38.Is 6961 divisible by 29?
  39. 39.Is 45044 divisible by 30?
  40. 40.Is 79700 divisible by 20?

Answer key

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

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