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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 312 · 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 131657 divisible by 19?
  2. 2.Is 30371 divisible by 5?
  3. 3.Is 62137 divisible by 17?
  4. 4.Is 9630 divisible by 19?
  5. 5.Is 22572 divisible by 19?
  6. 6.Is 122460 divisible by 30?
  7. 7.Is 10949 divisible by 20?
  8. 8.Is 62369 divisible by 19?
  9. 9.Is 76317 divisible by 11?
  10. 10.Is 55944 divisible by 12?
  11. 11.Is 69003 divisible by 11?
  12. 12.Is 131879 divisible by 20?
  13. 13.Is 75225 divisible by 15?
  14. 14.Is 7607 divisible by 15?
  15. 15.Is 47719 divisible by 17?
  16. 16.Is 8212 divisible by 2?
  17. 17.Is 2712 divisible by 20?
  18. 18.Is 28555 divisible by 6?
  19. 19.Is 7201 divisible by 19?
  20. 20.Is 4232 divisible by 4?
  21. 21.Is 8878 divisible by 5?
  22. 22.Is 116262 divisible by 20?
  23. 23.Is 26320 divisible by 7?
  24. 24.Is 26152 divisible by 6?
  25. 25.Is 31362 divisible by 6?
  26. 26.Is 69323 divisible by 23?
  27. 27.Is 5126 divisible by 12?
  28. 28.Is 19693 divisible by 3?
  29. 29.Is 10591 divisible by 17?
  30. 30.Is 14719 divisible by 29?
  31. 31.Is 27670 divisible by 5?
  32. 32.Is 23352 divisible by 7?
  33. 33.Is 37145 divisible by 19?
  34. 34.Is 108603 divisible by 30?
  35. 35.Is 56096 divisible by 15?
  36. 36.Is 610 divisible by 10?
  37. 37.Is 4150 divisible by 10?
  38. 38.Is 14546 divisible by 7?
  39. 39.Is 33677 divisible by 7?
  40. 40.Is 41316 divisible by 12?

Answer key

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

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