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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 696 · 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 8696 divisible by 2?
  2. 2.Is 61887 divisible by 10?
  3. 3.Is 5698 divisible by 3?
  4. 4.Is 1992 divisible by 2?
  5. 5.Is 7649 divisible by 5?
  6. 6.Is 23015 divisible by 29?
  7. 7.Is 19755 divisible by 8?
  8. 8.Is 6116 divisible by 17?
  9. 9.Is 18622 divisible by 4?
  10. 10.Is 32292 divisible by 9?
  11. 11.Is 76735 divisible by 23?
  12. 12.Is 40320 divisible by 12?
  13. 13.Is 111587 divisible by 19?
  14. 14.Is 20710 divisible by 5?
  15. 15.Is 22600 divisible by 4?
  16. 16.Is 44132 divisible by 11?
  17. 17.Is 94965 divisible by 15?
  18. 18.Is 70927 divisible by 20?
  19. 19.Is 22847 divisible by 23?
  20. 20.Is 52050 divisible by 15?
  21. 21.Is 10991 divisible by 2?
  22. 22.Is 66056 divisible by 23?
  23. 23.Is 42536 divisible by 8?
  24. 24.Is 30443 divisible by 7?
  25. 25.Is 76240 divisible by 20?
  26. 26.Is 32293 divisible by 23?
  27. 27.Is 4513 divisible by 24?
  28. 28.Is 96385 divisible by 18?
  29. 29.Is 10308 divisible by 6?
  30. 30.Is 91446 divisible by 20?
  31. 31.Is 3420 divisible by 12?
  32. 32.Is 1454 divisible by 4?
  33. 33.Is 43264 divisible by 8?
  34. 34.Is 5049 divisible by 11?
  35. 35.Is 2278 divisible by 17?
  36. 36.Is 18792 divisible by 3?
  37. 37.Is 31179 divisible by 19?
  38. 38.Is 118500 divisible by 30?
  39. 39.Is 21447 divisible by 12?
  40. 40.Is 116070 divisible by 30?

Answer key

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

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