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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 654 · 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 25550 divisible by 10?
  2. 2.Is 130169 divisible by 23?
  3. 3.Is 33991 divisible by 19?
  4. 4.Is 25604 divisible by 6?
  5. 5.Is 53843 divisible by 10?
  6. 6.Is 48440 divisible by 7?
  7. 7.Is 33388 divisible by 17?
  8. 8.Is 113160 divisible by 30?
  9. 9.Is 50565 divisible by 10?
  10. 10.Is 69365 divisible by 17?
  11. 11.Is 35974 divisible by 12?
  12. 12.Is 18927 divisible by 5?
  13. 13.Is 44936 divisible by 8?
  14. 14.Is 113699 divisible by 18?
  15. 15.Is 12051 divisible by 3?
  16. 16.Is 7890 divisible by 6?
  17. 17.Is 6015 divisible by 3?
  18. 18.Is 58605 divisible by 15?
  19. 19.Is 17358 divisible by 12?
  20. 20.Is 11990 divisible by 4?
  21. 21.Is 8122 divisible by 2?
  22. 22.Is 67374 divisible by 19?
  23. 23.Is 13177 divisible by 2?
  24. 24.Is 65113 divisible by 19?
  25. 25.Is 38304 divisible by 7?
  26. 26.Is 72391 divisible by 15?
  27. 27.Is 49654 divisible by 11?
  28. 28.Is 89410 divisible by 24?
  29. 29.Is 54637 divisible by 8?
  30. 30.Is 19796 divisible by 4?
  31. 31.Is 29332 divisible by 24?
  32. 32.Is 23886 divisible by 6?
  33. 33.Is 114930 divisible by 18?
  34. 34.Is 94690 divisible by 17?
  35. 35.Is 121545 divisible by 20?
  36. 36.Is 59002 divisible by 13?
  37. 37.Is 7551 divisible by 6?
  38. 38.Is 54587 divisible by 17?
  39. 39.Is 130728 divisible by 24?
  40. 40.Is 46163 divisible by 15?

Answer key

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

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