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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 596 · 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 48084 divisible by 19?
  2. 2.Is 5898 divisible by 6?
  3. 3.Is 3615 divisible by 15?
  4. 4.Is 13410 divisible by 9?
  5. 5.Is 19260 divisible by 4?
  6. 6.Is 11900 divisible by 10?
  7. 7.Is 100848 divisible by 30?
  8. 8.Is 65595 divisible by 10?
  9. 9.Is 20198 divisible by 18?
  10. 10.Is 110112 divisible by 24?
  11. 11.Is 15846 divisible by 9?
  12. 12.Is 41830 divisible by 10?
  13. 13.Is 147378 divisible by 24?
  14. 14.Is 7192 divisible by 7?
  15. 15.Is 20104 divisible by 24?
  16. 16.Is 10682 divisible by 3?
  17. 17.Is 34189 divisible by 7?
  18. 18.Is 98142 divisible by 20?
  19. 19.Is 132168 divisible by 24?
  20. 20.Is 20337 divisible by 15?
  21. 21.Is 7165 divisible by 5?
  22. 22.Is 2741 divisible by 6?
  23. 23.Is 8856 divisible by 4?
  24. 24.Is 82834 divisible by 15?
  25. 25.Is 13968 divisible by 8?
  26. 26.Is 2355 divisible by 5?
  27. 27.Is 54890 divisible by 11?
  28. 28.Is 21592 divisible by 8?
  29. 29.Is 16218 divisible by 3?
  30. 30.Is 919 divisible by 7?
  31. 31.Is 22111 divisible by 4?
  32. 32.Is 175073 divisible by 29?
  33. 33.Is 26110 divisible by 9?
  34. 34.Is 14176 divisible by 6?
  35. 35.Is 405 divisible by 4?
  36. 36.Is 4518 divisible by 2?
  37. 37.Is 32625 divisible by 11?
  38. 38.Is 131280 divisible by 20?
  39. 39.Is 135480 divisible by 30?
  40. 40.Is 127533 divisible by 20?

Answer key

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

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