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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 598 · 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 30738 divisible by 6?
  2. 2.Is 8400 divisible by 12?
  3. 3.Is 30453 divisible by 17?
  4. 4.Is 8412 divisible by 15?
  5. 5.Is 1633 divisible by 24?
  6. 6.Is 37786 divisible by 6?
  7. 7.Is 2680 divisible by 11?
  8. 8.Is 10419 divisible by 5?
  9. 9.Is 25399 divisible by 12?
  10. 10.Is 24529 divisible by 6?
  11. 11.Is 1529 divisible by 11?
  12. 12.Is 75168 divisible by 18?
  13. 13.Is 202260 divisible by 29?
  14. 14.Is 129200 divisible by 19?
  15. 15.Is 201318 divisible by 29?
  16. 16.Is 11318 divisible by 2?
  17. 17.Is 6709 divisible by 8?
  18. 18.Is 9067 divisible by 4?
  19. 19.Is 39360 divisible by 20?
  20. 20.Is 93705 divisible by 15?
  21. 21.Is 35862 divisible by 18?
  22. 22.Is 57190 divisible by 10?
  23. 23.Is 15660 divisible by 9?
  24. 24.Is 8139 divisible by 9?
  25. 25.Is 55307 divisible by 13?
  26. 26.Is 15492 divisible by 3?
  27. 27.Is 9515 divisible by 11?
  28. 28.Is 126702 divisible by 30?
  29. 29.Is 5292 divisible by 4?
  30. 30.Is 10454 divisible by 2?
  31. 31.Is 67279 divisible by 18?
  32. 32.Is 15595 divisible by 5?
  33. 33.Is 62900 divisible by 10?
  34. 34.Is 16472 divisible by 20?
  35. 35.Is 35498 divisible by 30?
  36. 36.Is 65559 divisible by 13?
  37. 37.Is 20878 divisible by 5?
  38. 38.Is 196794 divisible by 29?
  39. 39.Is 7643 divisible by 2?
  40. 40.Is 7564 divisible by 11?

Answer key

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

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