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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 544 · 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 42622 divisible by 10?
  2. 2.Is 2956 divisible by 4?
  3. 3.Is 36260 divisible by 7?
  4. 4.Is 13322 divisible by 2?
  5. 5.Is 111220 divisible by 20?
  6. 6.Is 30660 divisible by 6?
  7. 7.Is 14160 divisible by 15?
  8. 8.Is 24254 divisible by 15?
  9. 9.Is 8518 divisible by 4?
  10. 10.Is 5113 divisible by 12?
  11. 11.Is 23812 divisible by 29?
  12. 12.Is 41325 divisible by 13?
  13. 13.Is 33804 divisible by 9?
  14. 14.Is 5510 divisible by 5?
  15. 15.Is 64961 divisible by 13?
  16. 16.Is 87003 divisible by 18?
  17. 17.Is 104700 divisible by 15?
  18. 18.Is 2875 divisible by 2?
  19. 19.Is 7474 divisible by 2?
  20. 20.Is 41973 divisible by 17?
  21. 21.Is 30435 divisible by 5?
  22. 22.Is 92024 divisible by 19?
  23. 23.Is 32734 divisible by 13?
  24. 24.Is 7725 divisible by 3?
  25. 25.Is 106843 divisible by 19?
  26. 26.Is 79386 divisible by 17?
  27. 27.Is 7062 divisible by 29?
  28. 28.Is 13744 divisible by 4?
  29. 29.Is 26404 divisible by 23?
  30. 30.Is 117378 divisible by 18?
  31. 31.Is 56386 divisible by 11?
  32. 32.Is 18007 divisible by 3?
  33. 33.Is 4035 divisible by 5?
  34. 34.Is 74523 divisible by 15?
  35. 35.Is 4992 divisible by 6?
  36. 36.Is 170475 divisible by 30?
  37. 37.Is 108318 divisible by 18?
  38. 38.Is 22848 divisible by 8?
  39. 39.Is 22560 divisible by 15?
  40. 40.Is 123924 divisible by 23?

Answer key

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

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