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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 361 · 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 36621 divisible by 13?
  2. 2.Is 6804 divisible by 7?
  3. 3.Is 30345 divisible by 7?
  4. 4.Is 22169 divisible by 7?
  5. 5.Is 40838 divisible by 6?
  6. 6.Is 46821 divisible by 7?
  7. 7.Is 121788 divisible by 18?
  8. 8.Is 3049 divisible by 2?
  9. 9.Is 3756 divisible by 3?
  10. 10.Is 81043 divisible by 18?
  11. 11.Is 23193 divisible by 4?
  12. 12.Is 49010 divisible by 13?
  13. 13.Is 109231 divisible by 19?
  14. 14.Is 20756 divisible by 5?
  15. 15.Is 17716 divisible by 13?
  16. 16.Is 11191 divisible by 19?
  17. 17.Is 32980 divisible by 17?
  18. 18.Is 170084 divisible by 29?
  19. 19.Is 67826 divisible by 11?
  20. 20.Is 52840 divisible by 8?
  21. 21.Is 5406 divisible by 10?
  22. 22.Is 32450 divisible by 17?
  23. 23.Is 12556 divisible by 13?
  24. 24.Is 135923 divisible by 29?
  25. 25.Is 121267 divisible by 29?
  26. 26.Is 70142 divisible by 17?
  27. 27.Is 103832 divisible by 30?
  28. 28.Is 9939 divisible by 3?
  29. 29.Is 26362 divisible by 8?
  30. 30.Is 5090 divisible by 18?
  31. 31.Is 66862 divisible by 18?
  32. 32.Is 55140 divisible by 23?
  33. 33.Is 7811 divisible by 2?
  34. 34.Is 79224 divisible by 24?
  35. 35.Is 26763 divisible by 11?
  36. 36.Is 41115 divisible by 23?
  37. 37.Is 64380 divisible by 30?
  38. 38.Is 18660 divisible by 6?
  39. 39.Is 33390 divisible by 6?
  40. 40.Is 77639 divisible by 15?

Answer key

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

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