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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 911 · 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 1007 divisible by 19?
  2. 2.Is 11741 divisible by 2?
  3. 3.Is 161448 divisible by 24?
  4. 4.Is 102554 divisible by 18?
  5. 5.Is 5730 divisible by 15?
  6. 6.Is 121634 divisible by 20?
  7. 7.Is 104051 divisible by 19?
  8. 8.Is 66387 divisible by 23?
  9. 9.Is 70180 divisible by 29?
  10. 10.Is 6958 divisible by 7?
  11. 11.Is 143863 divisible by 23?
  12. 12.Is 6282 divisible by 3?
  13. 13.Is 90512 divisible by 23?
  14. 14.Is 87704 divisible by 19?
  15. 15.Is 23366 divisible by 7?
  16. 16.Is 17662 divisible by 4?
  17. 17.Is 42278 divisible by 11?
  18. 18.Is 3315 divisible by 2?
  19. 19.Is 68991 divisible by 29?
  20. 20.Is 27374 divisible by 4?
  21. 21.Is 19134 divisible by 18?
  22. 22.Is 103474 divisible by 18?
  23. 23.Is 5639 divisible by 6?
  24. 24.Is 32820 divisible by 20?
  25. 25.Is 3114 divisible by 5?
  26. 26.Is 46488 divisible by 12?
  27. 27.Is 18240 divisible by 5?
  28. 28.Is 16864 divisible by 4?
  29. 29.Is 105373 divisible by 19?
  30. 30.Is 1860 divisible by 13?
  31. 31.Is 47360 divisible by 20?
  32. 32.Is 12254 divisible by 6?
  33. 33.Is 55237 divisible by 13?
  34. 34.Is 103700 divisible by 15?
  35. 35.Is 65274 divisible by 23?
  36. 36.Is 68071 divisible by 20?
  37. 37.Is 15153 divisible by 11?
  38. 38.Is 104761 divisible by 18?
  39. 39.Is 85126 divisible by 15?
  40. 40.Is 27703 divisible by 13?

Answer key

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

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