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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 298 · 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 5563 divisible by 10?
  2. 2.Is 19872 divisible by 6?
  3. 3.Is 1613 divisible by 20?
  4. 4.Is 14346 divisible by 7?
  5. 5.Is 34884 divisible by 9?
  6. 6.Is 140887 divisible by 29?
  7. 7.Is 30804 divisible by 6?
  8. 8.Is 8701 divisible by 2?
  9. 9.Is 9895 divisible by 15?
  10. 10.Is 115431 divisible by 18?
  11. 11.Is 15817 divisible by 6?
  12. 12.Is 24465 divisible by 5?
  13. 13.Is 49368 divisible by 17?
  14. 14.Is 33733 divisible by 7?
  15. 15.Is 6196 divisible by 4?
  16. 16.Is 56062 divisible by 17?
  17. 17.Is 51477 divisible by 23?
  18. 18.Is 52713 divisible by 20?
  19. 19.Is 10956 divisible by 3?
  20. 20.Is 143359 divisible by 23?
  21. 21.Is 31600 divisible by 13?
  22. 22.Is 2140 divisible by 2?
  23. 23.Is 17570 divisible by 10?
  24. 24.Is 36068 divisible by 8?
  25. 25.Is 6937 divisible by 7?
  26. 26.Is 12417 divisible by 2?
  27. 27.Is 13245 divisible by 10?
  28. 28.Is 1981 divisible by 7?
  29. 29.Is 7728 divisible by 12?
  30. 30.Is 11552 divisible by 19?
  31. 31.Is 32748 divisible by 8?
  32. 32.Is 30337 divisible by 5?
  33. 33.Is 13379 divisible by 17?
  34. 34.Is 134186 divisible by 29?
  35. 35.Is 26462 divisible by 20?
  36. 36.Is 15143 divisible by 3?
  37. 37.Is 6657 divisible by 18?
  38. 38.Is 73493 divisible by 17?
  39. 39.Is 32021 divisible by 9?
  40. 40.Is 32666 divisible by 12?

Answer key

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

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