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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 478 · 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 61902 divisible by 18?
  2. 2.Is 30685 divisible by 17?
  3. 3.Is 25569 divisible by 11?
  4. 4.Is 50778 divisible by 29?
  5. 5.Is 10195 divisible by 2?
  6. 6.Is 9216 divisible by 30?
  7. 7.Is 9914 divisible by 10?
  8. 8.Is 5445 divisible by 15?
  9. 9.Is 92344 divisible by 17?
  10. 10.Is 24037 divisible by 13?
  11. 11.Is 10612 divisible by 3?
  12. 12.Is 5277 divisible by 3?
  13. 13.Is 4730 divisible by 10?
  14. 14.Is 15560 divisible by 3?
  15. 15.Is 16416 divisible by 4?
  16. 16.Is 2797 divisible by 2?
  17. 17.Is 20160 divisible by 6?
  18. 18.Is 22621 divisible by 30?
  19. 19.Is 7140 divisible by 17?
  20. 20.Is 10449 divisible by 7?
  21. 21.Is 20019 divisible by 7?
  22. 22.Is 19363 divisible by 17?
  23. 23.Is 19651 divisible by 7?
  24. 24.Is 24005 divisible by 5?
  25. 25.Is 96828 divisible by 17?
  26. 26.Is 2724 divisible by 11?
  27. 27.Is 118277 divisible by 23?
  28. 28.Is 19170 divisible by 4?
  29. 29.Is 4945 divisible by 3?
  30. 30.Is 55140 divisible by 30?
  31. 31.Is 103374 divisible by 30?
  32. 32.Is 15050 divisible by 5?
  33. 33.Is 17405 divisible by 17?
  34. 34.Is 35392 divisible by 11?
  35. 35.Is 125540 divisible by 20?
  36. 36.Is 15615 divisible by 3?
  37. 37.Is 78959 divisible by 23?
  38. 38.Is 25534 divisible by 17?
  39. 39.Is 103593 divisible by 23?
  40. 40.Is 108053 divisible by 19?

Answer key

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

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