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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 166 · 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 53632 divisible by 15?
  2. 2.Is 79117 divisible by 12?
  3. 3.Is 34896 divisible by 24?
  4. 4.Is 15322 divisible by 7?
  5. 5.Is 70650 divisible by 15?
  6. 6.Is 85901 divisible by 17?
  7. 7.Is 1453 divisible by 2?
  8. 8.Is 95675 divisible by 15?
  9. 9.Is 58051 divisible by 20?
  10. 10.Is 4369 divisible by 3?
  11. 11.Is 90457 divisible by 15?
  12. 12.Is 5373 divisible by 3?
  13. 13.Is 47563 divisible by 10?
  14. 14.Is 20219 divisible by 3?
  15. 15.Is 49822 divisible by 29?
  16. 16.Is 15042 divisible by 3?
  17. 17.Is 18498 divisible by 3?
  18. 18.Is 133435 divisible by 29?
  19. 19.Is 33013 divisible by 9?
  20. 20.Is 35640 divisible by 20?
  21. 21.Is 25300 divisible by 10?
  22. 22.Is 66290 divisible by 10?
  23. 23.Is 16424 divisible by 6?
  24. 24.Is 46472 divisible by 8?
  25. 25.Is 46616 divisible by 8?
  26. 26.Is 16517 divisible by 3?
  27. 27.Is 34741 divisible by 7?
  28. 28.Is 19914 divisible by 6?
  29. 29.Is 14905 divisible by 8?
  30. 30.Is 31895 divisible by 10?
  31. 31.Is 58681 divisible by 30?
  32. 32.Is 45110 divisible by 9?
  33. 33.Is 22026 divisible by 10?
  34. 34.Is 972 divisible by 2?
  35. 35.Is 135799 divisible by 29?
  36. 36.Is 29471 divisible by 10?
  37. 37.Is 764 divisible by 6?
  38. 38.Is 16669 divisible by 3?
  39. 39.Is 960 divisible by 12?
  40. 40.Is 3735 divisible by 3?

Answer key

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

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