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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 237 · 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 32470 divisible by 5?
  2. 2.Is 48091 divisible by 10?
  3. 3.Is 9765 divisible by 3?
  4. 4.Is 37872 divisible by 24?
  5. 5.Is 9669 divisible by 3?
  6. 6.Is 116841 divisible by 29?
  7. 7.Is 22800 divisible by 8?
  8. 8.Is 60874 divisible by 13?
  9. 9.Is 43877 divisible by 9?
  10. 10.Is 19424 divisible by 8?
  11. 11.Is 3411 divisible by 8?
  12. 12.Is 3434 divisible by 11?
  13. 13.Is 62269 divisible by 11?
  14. 14.Is 8948 divisible by 4?
  15. 15.Is 101175 divisible by 15?
  16. 16.Is 1084 divisible by 4?
  17. 17.Is 48430 divisible by 10?
  18. 18.Is 17822 divisible by 15?
  19. 19.Is 102196 divisible by 15?
  20. 20.Is 7099 divisible by 11?
  21. 21.Is 201513 divisible by 30?
  22. 22.Is 60541 divisible by 13?
  23. 23.Is 35820 divisible by 9?
  24. 24.Is 28066 divisible by 30?
  25. 25.Is 3354 divisible by 13?
  26. 26.Is 66727 divisible by 17?
  27. 27.Is 11067 divisible by 2?
  28. 28.Is 29966 divisible by 7?
  29. 29.Is 33994 divisible by 5?
  30. 30.Is 100860 divisible by 15?
  31. 31.Is 10026 divisible by 5?
  32. 32.Is 106191 divisible by 23?
  33. 33.Is 18961 divisible by 4?
  34. 34.Is 26029 divisible by 7?
  35. 35.Is 55147 divisible by 19?
  36. 36.Is 26481 divisible by 13?
  37. 37.Is 11084 divisible by 18?
  38. 38.Is 31269 divisible by 7?
  39. 39.Is 6011 divisible by 3?
  40. 40.Is 33110 divisible by 5?

Answer key

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

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