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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 406 · 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 5604 divisible by 6?
  2. 2.Is 28167 divisible by 5?
  3. 3.Is 98199 divisible by 15?
  4. 4.Is 4720 divisible by 8?
  5. 5.Is 190095 divisible by 29?
  6. 6.Is 7038 divisible by 23?
  7. 7.Is 3949 divisible by 3?
  8. 8.Is 28325 divisible by 12?
  9. 9.Is 4990 divisible by 10?
  10. 10.Is 15288 divisible by 8?
  11. 11.Is 7728 divisible by 23?
  12. 12.Is 19734 divisible by 8?
  13. 13.Is 90271 divisible by 24?
  14. 14.Is 24290 divisible by 8?
  15. 15.Is 4112 divisible by 8?
  16. 16.Is 46424 divisible by 8?
  17. 17.Is 10368 divisible by 3?
  18. 18.Is 147554 divisible by 30?
  19. 19.Is 101088 divisible by 18?
  20. 20.Is 82596 divisible by 12?
  21. 21.Is 103438 divisible by 23?
  22. 22.Is 23669 divisible by 10?
  23. 23.Is 51753 divisible by 8?
  24. 24.Is 60522 divisible by 9?
  25. 25.Is 51617 divisible by 9?
  26. 26.Is 7928 divisible by 8?
  27. 27.Is 22350 divisible by 15?
  28. 28.Is 5812 divisible by 3?
  29. 29.Is 144153 divisible by 24?
  30. 30.Is 13541 divisible by 12?
  31. 31.Is 85787 divisible by 23?
  32. 32.Is 1317 divisible by 4?
  33. 33.Is 25267 divisible by 4?
  34. 34.Is 18700 divisible by 6?
  35. 35.Is 83749 divisible by 20?
  36. 36.Is 64680 divisible by 20?
  37. 37.Is 31229 divisible by 11?
  38. 38.Is 113176 divisible by 20?
  39. 39.Is 125703 divisible by 20?
  40. 40.Is 33641 divisible by 12?

Answer key

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

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