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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 339 · 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 4653 divisible by 15?
  2. 2.Is 20651 divisible by 29?
  3. 3.Is 51966 divisible by 9?
  4. 4.Is 22083 divisible by 17?
  5. 5.Is 20277 divisible by 8?
  6. 6.Is 97631 divisible by 17?
  7. 7.Is 4482 divisible by 3?
  8. 8.Is 67803 divisible by 19?
  9. 9.Is 79557 divisible by 23?
  10. 10.Is 8098 divisible by 17?
  11. 11.Is 169433 divisible by 29?
  12. 12.Is 20443 divisible by 5?
  13. 13.Is 24240 divisible by 8?
  14. 14.Is 22536 divisible by 8?
  15. 15.Is 90015 divisible by 15?
  16. 16.Is 51323 divisible by 23?
  17. 17.Is 129369 divisible by 29?
  18. 18.Is 63479 divisible by 19?
  19. 19.Is 29996 divisible by 23?
  20. 20.Is 1087 divisible by 13?
  21. 21.Is 55635 divisible by 15?
  22. 22.Is 5856 divisible by 8?
  23. 23.Is 40629 divisible by 18?
  24. 24.Is 16704 divisible by 10?
  25. 25.Is 67704 divisible by 13?
  26. 26.Is 135791 divisible by 24?
  27. 27.Is 57939 divisible by 10?
  28. 28.Is 19725 divisible by 3?
  29. 29.Is 36256 divisible by 29?
  30. 30.Is 19613 divisible by 29?
  31. 31.Is 31780 divisible by 20?
  32. 32.Is 44632 divisible by 10?
  33. 33.Is 2243 divisible by 8?
  34. 34.Is 33001 divisible by 6?
  35. 35.Is 157035 divisible by 29?
  36. 36.Is 12058 divisible by 9?
  37. 37.Is 1428 divisible by 23?
  38. 38.Is 9402 divisible by 3?
  39. 39.Is 9300 divisible by 3?
  40. 40.Is 4759 divisible by 30?

Answer key

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

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