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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 667 · 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 201510 divisible by 30?
  2. 2.Is 25025 divisible by 5?
  3. 3.Is 14834 divisible by 9?
  4. 4.Is 34476 divisible by 6?
  5. 5.Is 58995 divisible by 23?
  6. 6.Is 126558 divisible by 24?
  7. 7.Is 19614 divisible by 10?
  8. 8.Is 19318 divisible by 15?
  9. 9.Is 29691 divisible by 9?
  10. 10.Is 33555 divisible by 5?
  11. 11.Is 20339 divisible by 11?
  12. 12.Is 34018 divisible by 7?
  13. 13.Is 134040 divisible by 30?
  14. 14.Is 7953 divisible by 11?
  15. 15.Is 2326 divisible by 19?
  16. 16.Is 50125 divisible by 8?
  17. 17.Is 84656 divisible by 13?
  18. 18.Is 7095 divisible by 12?
  19. 19.Is 14593 divisible by 5?
  20. 20.Is 63912 divisible by 19?
  21. 21.Is 4705 divisible by 9?
  22. 22.Is 26772 divisible by 12?
  23. 23.Is 40842 divisible by 24?
  24. 24.Is 21440 divisible by 20?
  25. 25.Is 16367 divisible by 13?
  26. 26.Is 40164 divisible by 9?
  27. 27.Is 8064 divisible by 17?
  28. 28.Is 159686 divisible by 24?
  29. 29.Is 10060 divisible by 4?
  30. 30.Is 2652 divisible by 13?
  31. 31.Is 5391 divisible by 4?
  32. 32.Is 71662 divisible by 13?
  33. 33.Is 51696 divisible by 24?
  34. 34.Is 2923 divisible by 2?
  35. 35.Is 79665 divisible by 12?
  36. 36.Is 64548 divisible by 18?
  37. 37.Is 50932 divisible by 10?
  38. 38.Is 34943 divisible by 12?
  39. 39.Is 35130 divisible by 20?
  40. 40.Is 122217 divisible by 23?

Answer key

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

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