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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 225 · 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 25563 divisible by 17?
  2. 2.Is 35614 divisible by 8?
  3. 3.Is 9047 divisible by 8?
  4. 4.Is 51525 divisible by 15?
  5. 5.Is 16758 divisible by 12?
  6. 6.Is 14202 divisible by 9?
  7. 7.Is 96615 divisible by 18?
  8. 8.Is 67373 divisible by 23?
  9. 9.Is 146220 divisible by 24?
  10. 10.Is 18209 divisible by 6?
  11. 11.Is 109800 divisible by 24?
  12. 12.Is 55327 divisible by 12?
  13. 13.Is 8082 divisible by 18?
  14. 14.Is 42748 divisible by 29?
  15. 15.Is 75739 divisible by 23?
  16. 16.Is 89940 divisible by 15?
  17. 17.Is 28492 divisible by 17?
  18. 18.Is 81900 divisible by 30?
  19. 19.Is 13249 divisible by 8?
  20. 20.Is 5108 divisible by 18?
  21. 21.Is 96030 divisible by 30?
  22. 22.Is 160320 divisible by 30?
  23. 23.Is 10161 divisible by 4?
  24. 24.Is 39168 divisible by 20?
  25. 25.Is 27338 divisible by 19?
  26. 26.Is 27855 divisible by 10?
  27. 27.Is 71524 divisible by 18?
  28. 28.Is 93175 divisible by 18?
  29. 29.Is 12813 divisible by 3?
  30. 30.Is 86296 divisible by 23?
  31. 31.Is 48805 divisible by 7?
  32. 32.Is 2925 divisible by 13?
  33. 33.Is 6111 divisible by 15?
  34. 34.Is 28000 divisible by 20?
  35. 35.Is 53624 divisible by 15?
  36. 36.Is 102942 divisible by 24?
  37. 37.Is 13077 divisible by 7?
  38. 38.Is 6577 divisible by 4?
  39. 39.Is 79655 divisible by 18?
  40. 40.Is 79125 divisible by 15?

Answer key

  1. no
  2. no
  3. no
  4. yes
  5. no
  6. yes
  7. no
  8. no
  9. no
  10. no
  11. yes
  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. no
  25. no
  26. no
  27. no
  28. no
  29. yes
  30. yes
  31. no
  32. yes
  33. no
  34. yes
  35. no
  36. no
  37. no
  38. no
  39. no
  40. yes

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