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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 44 · 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 153515 divisible by 23?
  2. 2.Is 80697 divisible by 24?
  3. 3.Is 17652 divisible by 15?
  4. 4.Is 19560 divisible by 20?
  5. 5.Is 37098 divisible by 8?
  6. 6.Is 22909 divisible by 6?
  7. 7.Is 27022 divisible by 7?
  8. 8.Is 7820 divisible by 3?
  9. 9.Is 483 divisible by 15?
  10. 10.Is 17622 divisible by 6?
  11. 11.Is 11172 divisible by 7?
  12. 12.Is 44894 divisible by 23?
  13. 13.Is 16300 divisible by 10?
  14. 14.Is 4461 divisible by 2?
  15. 15.Is 16561 divisible by 4?
  16. 16.Is 14616 divisible by 6?
  17. 17.Is 25897 divisible by 12?
  18. 18.Is 17452 divisible by 9?
  19. 19.Is 21852 divisible by 18?
  20. 20.Is 95868 divisible by 17?
  21. 21.Is 110164 divisible by 18?
  22. 22.Is 9810 divisible by 10?
  23. 23.Is 13050 divisible by 29?
  24. 24.Is 55746 divisible by 15?
  25. 25.Is 56919 divisible by 9?
  26. 26.Is 9740 divisible by 20?
  27. 27.Is 78242 divisible by 19?
  28. 28.Is 5116 divisible by 17?
  29. 29.Is 3636 divisible by 3?
  30. 30.Is 1777 divisible by 4?
  31. 31.Is 31465 divisible by 29?
  32. 32.Is 47137 divisible by 7?
  33. 33.Is 13148 divisible by 19?
  34. 34.Is 24475 divisible by 5?
  35. 35.Is 8387 divisible by 6?
  36. 36.Is 56710 divisible by 18?
  37. 37.Is 80176 divisible by 18?
  38. 38.Is 10753 divisible by 2?
  39. 39.Is 40679 divisible by 19?
  40. 40.Is 24488 divisible by 7?

Answer key

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

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