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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 543 · 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 5820 divisible by 4?
  2. 2.Is 22147 divisible by 6?
  3. 3.Is 81702 divisible by 18?
  4. 4.Is 71190 divisible by 12?
  5. 5.Is 194700 divisible by 30?
  6. 6.Is 47642 divisible by 19?
  7. 7.Is 70888 divisible by 15?
  8. 8.Is 112211 divisible by 19?
  9. 9.Is 172943 divisible by 29?
  10. 10.Is 24840 divisible by 18?
  11. 11.Is 38196 divisible by 12?
  12. 12.Is 6319 divisible by 5?
  13. 13.Is 74862 divisible by 13?
  14. 14.Is 23837 divisible by 4?
  15. 15.Is 10368 divisible by 3?
  16. 16.Is 54324 divisible by 18?
  17. 17.Is 48580 divisible by 10?
  18. 18.Is 5558 divisible by 6?
  19. 19.Is 46158 divisible by 9?
  20. 20.Is 13479 divisible by 3?
  21. 21.Is 19494 divisible by 5?
  22. 22.Is 37662 divisible by 6?
  23. 23.Is 6327 divisible by 19?
  24. 24.Is 28188 divisible by 29?
  25. 25.Is 14615 divisible by 5?
  26. 26.Is 30085 divisible by 7?
  27. 27.Is 81245 divisible by 18?
  28. 28.Is 6154 divisible by 20?
  29. 29.Is 7946 divisible by 4?
  30. 30.Is 14679 divisible by 9?
  31. 31.Is 38444 divisible by 6?
  32. 32.Is 14181 divisible by 29?
  33. 33.Is 8626 divisible by 3?
  34. 34.Is 17357 divisible by 17?
  35. 35.Is 1248 divisible by 24?
  36. 36.Is 29906 divisible by 8?
  37. 37.Is 43563 divisible by 13?
  38. 38.Is 23883 divisible by 8?
  39. 39.Is 51768 divisible by 24?
  40. 40.Is 19805 divisible by 7?

Answer key

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

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