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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 682 · 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 114680 divisible by 20?
  2. 2.Is 104134 divisible by 30?
  3. 3.Is 2673 divisible by 19?
  4. 4.Is 17946 divisible by 6?
  5. 5.Is 15208 divisible by 8?
  6. 6.Is 19278 divisible by 6?
  7. 7.Is 44302 divisible by 7?
  8. 8.Is 29531 divisible by 8?
  9. 9.Is 42972 divisible by 12?
  10. 10.Is 893 divisible by 2?
  11. 11.Is 45211 divisible by 29?
  12. 12.Is 90946 divisible by 18?
  13. 13.Is 25408 divisible by 9?
  14. 14.Is 126000 divisible by 18?
  15. 15.Is 19757 divisible by 23?
  16. 16.Is 114579 divisible by 29?
  17. 17.Is 107491 divisible by 17?
  18. 18.Is 3126 divisible by 6?
  19. 19.Is 80951 divisible by 13?
  20. 20.Is 24507 divisible by 9?
  21. 21.Is 36548 divisible by 6?
  22. 22.Is 27413 divisible by 6?
  23. 23.Is 43635 divisible by 9?
  24. 24.Is 40952 divisible by 8?
  25. 25.Is 5770 divisible by 10?
  26. 26.Is 5830 divisible by 5?
  27. 27.Is 78324 divisible by 12?
  28. 28.Is 1995 divisible by 3?
  29. 29.Is 11310 divisible by 6?
  30. 30.Is 139896 divisible by 29?
  31. 31.Is 5212 divisible by 2?
  32. 32.Is 52300 divisible by 20?
  33. 33.Is 122724 divisible by 18?
  34. 34.Is 23306 divisible by 19?
  35. 35.Is 93534 divisible by 17?
  36. 36.Is 18654 divisible by 3?
  37. 37.Is 12920 divisible by 17?
  38. 38.Is 19721 divisible by 4?
  39. 39.Is 22681 divisible by 4?
  40. 40.Is 7091 divisible by 2?

Answer key

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

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