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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 622 · 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 2601 divisible by 4?
  2. 2.Is 111546 divisible by 18?
  3. 3.Is 67249 divisible by 13?
  4. 4.Is 94993 divisible by 18?
  5. 5.Is 12455 divisible by 2?
  6. 6.Is 33807 divisible by 10?
  7. 7.Is 46123 divisible by 11?
  8. 8.Is 35415 divisible by 9?
  9. 9.Is 34315 divisible by 18?
  10. 10.Is 217 divisible by 3?
  11. 11.Is 4110 divisible by 3?
  12. 12.Is 9852 divisible by 3?
  13. 13.Is 1702 divisible by 2?
  14. 14.Is 17565 divisible by 3?
  15. 15.Is 6728 divisible by 4?
  16. 16.Is 2607 divisible by 17?
  17. 17.Is 889 divisible by 9?
  18. 18.Is 40576 divisible by 12?
  19. 19.Is 59983 divisible by 11?
  20. 20.Is 800 divisible by 2?
  21. 21.Is 55332 divisible by 19?
  22. 22.Is 85098 divisible by 13?
  23. 23.Is 48766 divisible by 18?
  24. 24.Is 64110 divisible by 23?
  25. 25.Is 470 divisible by 3?
  26. 26.Is 79871 divisible by 19?
  27. 27.Is 2492 divisible by 7?
  28. 28.Is 146409 divisible by 30?
  29. 29.Is 28385 divisible by 8?
  30. 30.Is 9350 divisible by 2?
  31. 31.Is 132984 divisible by 24?
  32. 32.Is 73929 divisible by 19?
  33. 33.Is 90804 divisible by 23?
  34. 34.Is 33828 divisible by 8?
  35. 35.Is 34130 divisible by 5?
  36. 36.Is 15420 divisible by 15?
  37. 37.Is 43365 divisible by 7?
  38. 38.Is 96953 divisible by 30?
  39. 39.Is 31066 divisible by 5?
  40. 40.Is 4682 divisible by 7?

Answer key

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

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