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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 91 · 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 23608 divisible by 8?
  2. 2.Is 10130 divisible by 10?
  3. 3.Is 83199 divisible by 29?
  4. 4.Is 55132 divisible by 15?
  5. 5.Is 46168 divisible by 8?
  6. 6.Is 64480 divisible by 10?
  7. 7.Is 113114 divisible by 23?
  8. 8.Is 57190 divisible by 18?
  9. 9.Is 45129 divisible by 9?
  10. 10.Is 19110 divisible by 15?
  11. 11.Is 5639 divisible by 10?
  12. 12.Is 9120 divisible by 12?
  13. 13.Is 22023 divisible by 6?
  14. 14.Is 287 divisible by 3?
  15. 15.Is 46804 divisible by 18?
  16. 16.Is 42402 divisible by 8?
  17. 17.Is 31528 divisible by 7?
  18. 18.Is 1363 divisible by 2?
  19. 19.Is 53746 divisible by 15?
  20. 20.Is 105108 divisible by 19?
  21. 21.Is 31644 divisible by 23?
  22. 22.Is 3071 divisible by 17?
  23. 23.Is 31521 divisible by 19?
  24. 24.Is 44213 divisible by 19?
  25. 25.Is 13914 divisible by 3?
  26. 26.Is 33420 divisible by 15?
  27. 27.Is 19873 divisible by 19?
  28. 28.Is 9705 divisible by 3?
  29. 29.Is 63020 divisible by 19?
  30. 30.Is 46636 divisible by 17?
  31. 31.Is 79846 divisible by 20?
  32. 32.Is 26615 divisible by 4?
  33. 33.Is 37389 divisible by 6?
  34. 34.Is 16598 divisible by 30?
  35. 35.Is 11988 divisible by 6?
  36. 36.Is 25950 divisible by 30?
  37. 37.Is 15173 divisible by 4?
  38. 38.Is 3960 divisible by 5?
  39. 39.Is 6948 divisible by 6?
  40. 40.Is 37988 divisible by 29?

Answer key

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

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