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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 683 · 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 142493 divisible by 23?
  2. 2.Is 47912 divisible by 10?
  3. 3.Is 2570 divisible by 5?
  4. 4.Is 193401 divisible by 29?
  5. 5.Is 2610 divisible by 5?
  6. 6.Is 62595 divisible by 15?
  7. 7.Is 69669 divisible by 17?
  8. 8.Is 31369 divisible by 13?
  9. 9.Is 23359 divisible by 13?
  10. 10.Is 44294 divisible by 23?
  11. 11.Is 58961 divisible by 23?
  12. 12.Is 16140 divisible by 15?
  13. 13.Is 14841 divisible by 17?
  14. 14.Is 42322 divisible by 7?
  15. 15.Is 18203 divisible by 6?
  16. 16.Is 24710 divisible by 15?
  17. 17.Is 12678 divisible by 11?
  18. 18.Is 30274 divisible by 17?
  19. 19.Is 53712 divisible by 9?
  20. 20.Is 113700 divisible by 18?
  21. 21.Is 39120 divisible by 12?
  22. 22.Is 23506 divisible by 13?
  23. 23.Is 6296 divisible by 8?
  24. 24.Is 21783 divisible by 18?
  25. 25.Is 91776 divisible by 19?
  26. 26.Is 110178 divisible by 18?
  27. 27.Is 132000 divisible by 20?
  28. 28.Is 10167 divisible by 6?
  29. 29.Is 28920 divisible by 7?
  30. 30.Is 121104 divisible by 24?
  31. 31.Is 33630 divisible by 5?
  32. 32.Is 117938 divisible by 24?
  33. 33.Is 7084 divisible by 4?
  34. 34.Is 21471 divisible by 17?
  35. 35.Is 34843 divisible by 13?
  36. 36.Is 40861 divisible by 8?
  37. 37.Is 21984 divisible by 4?
  38. 38.Is 8343 divisible by 6?
  39. 39.Is 8365 divisible by 5?
  40. 40.Is 29547 divisible by 9?

Answer key

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

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