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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 831 · 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 18511 divisible by 23?
  2. 2.Is 26243 divisible by 15?
  3. 3.Is 52421 divisible by 9?
  4. 4.Is 11076 divisible by 2?
  5. 5.Is 13321 divisible by 5?
  6. 6.Is 8867 divisible by 30?
  7. 7.Is 36192 divisible by 8?
  8. 8.Is 36581 divisible by 20?
  9. 9.Is 17462 divisible by 30?
  10. 10.Is 86420 divisible by 20?
  11. 11.Is 18081 divisible by 9?
  12. 12.Is 7881 divisible by 6?
  13. 13.Is 40671 divisible by 12?
  14. 14.Is 36450 divisible by 7?
  15. 15.Is 35387 divisible by 6?
  16. 16.Is 83337 divisible by 17?
  17. 17.Is 45771 divisible by 11?
  18. 18.Is 41321 divisible by 13?
  19. 19.Is 6912 divisible by 3?
  20. 20.Is 3128 divisible by 15?
  21. 21.Is 18966 divisible by 6?
  22. 22.Is 40302 divisible by 9?
  23. 23.Is 73884 divisible by 15?
  24. 24.Is 1859 divisible by 2?
  25. 25.Is 21060 divisible by 12?
  26. 26.Is 13940 divisible by 13?
  27. 27.Is 35262 divisible by 11?
  28. 28.Is 100890 divisible by 18?
  29. 29.Is 8214 divisible by 3?
  30. 30.Is 14427 divisible by 5?
  31. 31.Is 13202 divisible by 5?
  32. 32.Is 15198 divisible by 6?
  33. 33.Is 9302 divisible by 5?
  34. 34.Is 38630 divisible by 20?
  35. 35.Is 61920 divisible by 10?
  36. 36.Is 59706 divisible by 23?
  37. 37.Is 104784 divisible by 29?
  38. 38.Is 34164 divisible by 12?
  39. 39.Is 42910 divisible by 9?
  40. 40.Is 110998 divisible by 18?

Answer key

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

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