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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 620 · 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 75813 divisible by 15?
  2. 2.Is 163502 divisible by 29?
  3. 3.Is 34420 divisible by 5?
  4. 4.Is 12179 divisible by 3?
  5. 5.Is 15243 divisible by 3?
  6. 6.Is 150473 divisible by 23?
  7. 7.Is 43046 divisible by 30?
  8. 8.Is 21950 divisible by 11?
  9. 9.Is 13385 divisible by 13?
  10. 10.Is 16123 divisible by 5?
  11. 11.Is 21174 divisible by 11?
  12. 12.Is 160888 divisible by 23?
  13. 13.Is 88140 divisible by 30?
  14. 14.Is 8021 divisible by 2?
  15. 15.Is 14787 divisible by 9?
  16. 16.Is 30855 divisible by 5?
  17. 17.Is 3607 divisible by 3?
  18. 18.Is 23537 divisible by 8?
  19. 19.Is 14562 divisible by 3?
  20. 20.Is 90414 divisible by 18?
  21. 21.Is 61126 divisible by 13?
  22. 22.Is 12120 divisible by 24?
  23. 23.Is 12857 divisible by 2?
  24. 24.Is 53000 divisible by 8?
  25. 25.Is 123507 divisible by 23?
  26. 26.Is 45900 divisible by 18?
  27. 27.Is 89897 divisible by 13?
  28. 28.Is 18154 divisible by 3?
  29. 29.Is 36083 divisible by 13?
  30. 30.Is 60370 divisible by 19?
  31. 31.Is 121192 divisible by 29?
  32. 32.Is 1374 divisible by 3?
  33. 33.Is 69321 divisible by 23?
  34. 34.Is 17052 divisible by 12?
  35. 35.Is 101453 divisible by 23?
  36. 36.Is 15054 divisible by 13?
  37. 37.Is 7272 divisible by 3?
  38. 38.Is 50184 divisible by 9?
  39. 39.Is 40487 divisible by 18?
  40. 40.Is 18985 divisible by 5?

Answer key

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

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