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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 687 · 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 39647 divisible by 8?
  2. 2.Is 37357 divisible by 6?
  3. 3.Is 37890 divisible by 9?
  4. 4.Is 3031 divisible by 2?
  5. 5.Is 13417 divisible by 8?
  6. 6.Is 6342 divisible by 2?
  7. 7.Is 72837 divisible by 15?
  8. 8.Is 10713 divisible by 2?
  9. 9.Is 6304 divisible by 8?
  10. 10.Is 53172 divisible by 11?
  11. 11.Is 29570 divisible by 17?
  12. 12.Is 32547 divisible by 19?
  13. 13.Is 95077 divisible by 17?
  14. 14.Is 6717 divisible by 3?
  15. 15.Is 164638 divisible by 24?
  16. 16.Is 19393 divisible by 11?
  17. 17.Is 510 divisible by 3?
  18. 18.Is 52800 divisible by 8?
  19. 19.Is 55740 divisible by 20?
  20. 20.Is 6170 divisible by 2?
  21. 21.Is 29488 divisible by 8?
  22. 22.Is 10712 divisible by 13?
  23. 23.Is 62519 divisible by 12?
  24. 24.Is 91635 divisible by 15?
  25. 25.Is 12591 divisible by 2?
  26. 26.Is 25454 divisible by 11?
  27. 27.Is 11964 divisible by 6?
  28. 28.Is 42036 divisible by 9?
  29. 29.Is 15654 divisible by 3?
  30. 30.Is 29680 divisible by 5?
  31. 31.Is 85644 divisible by 13?
  32. 32.Is 13758 divisible by 13?
  33. 33.Is 15751 divisible by 9?
  34. 34.Is 226 divisible by 3?
  35. 35.Is 160810 divisible by 24?
  36. 36.Is 42091 divisible by 7?
  37. 37.Is 52710 divisible by 10?
  38. 38.Is 5203 divisible by 2?
  39. 39.Is 26036 divisible by 4?
  40. 40.Is 48780 divisible by 20?

Answer key

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

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