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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 995 · 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 17940 divisible by 15?
  2. 2.Is 90083 divisible by 19?
  3. 3.Is 111060 divisible by 20?
  4. 4.Is 7012 divisible by 10?
  5. 5.Is 66600 divisible by 30?
  6. 6.Is 17592 divisible by 12?
  7. 7.Is 2760 divisible by 4?
  8. 8.Is 6986 divisible by 11?
  9. 9.Is 1548 divisible by 18?
  10. 10.Is 16005 divisible by 11?
  11. 11.Is 25060 divisible by 23?
  12. 12.Is 29153 divisible by 7?
  13. 13.Is 26130 divisible by 6?
  14. 14.Is 69504 divisible by 24?
  15. 15.Is 16881 divisible by 17?
  16. 16.Is 2510 divisible by 10?
  17. 17.Is 12519 divisible by 4?
  18. 18.Is 119140 divisible by 20?
  19. 19.Is 73370 divisible by 23?
  20. 20.Is 62818 divisible by 9?
  21. 21.Is 3984 divisible by 6?
  22. 22.Is 49935 divisible by 15?
  23. 23.Is 44824 divisible by 8?
  24. 24.Is 54125 divisible by 15?
  25. 25.Is 18786 divisible by 8?
  26. 26.Is 27990 divisible by 5?
  27. 27.Is 74008 divisible by 29?
  28. 28.Is 26539 divisible by 9?
  29. 29.Is 28681 divisible by 29?
  30. 30.Is 26164 divisible by 18?
  31. 31.Is 15688 divisible by 4?
  32. 32.Is 9841 divisible by 7?
  33. 33.Is 5263 divisible by 19?
  34. 34.Is 87376 divisible by 17?
  35. 35.Is 69652 divisible by 17?
  36. 36.Is 15803 divisible by 4?
  37. 37.Is 51536 divisible by 9?
  38. 38.Is 12120 divisible by 30?
  39. 39.Is 10367 divisible by 5?
  40. 40.Is 38860 divisible by 29?

Answer key

  1. yes
  2. no
  3. yes
  4. no
  5. yes
  6. yes
  7. yes
  8. no
  9. yes
  10. yes
  11. no
  12. no
  13. yes
  14. yes
  15. yes
  16. yes
  17. no
  18. yes
  19. yes
  20. no
  21. yes
  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. no
  35. no
  36. no
  37. no
  38. yes
  39. no
  40. yes

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