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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 137 · 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 2285 divisible by 12?
  2. 2.Is 54620 divisible by 20?
  3. 3.Is 90649 divisible by 19?
  4. 4.Is 10420 divisible by 12?
  5. 5.Is 25705 divisible by 17?
  6. 6.Is 9398 divisible by 2?
  7. 7.Is 3116 divisible by 8?
  8. 8.Is 23395 divisible by 9?
  9. 9.Is 61441 divisible by 18?
  10. 10.Is 29969 divisible by 23?
  11. 11.Is 12904 divisible by 3?
  12. 12.Is 156504 divisible by 24?
  13. 13.Is 62748 divisible by 19?
  14. 14.Is 31250 divisible by 10?
  15. 15.Is 45925 divisible by 8?
  16. 16.Is 5204 divisible by 8?
  17. 17.Is 20789 divisible by 3?
  18. 18.Is 146579 divisible by 23?
  19. 19.Is 8643 divisible by 3?
  20. 20.Is 4393 divisible by 3?
  21. 21.Is 27456 divisible by 7?
  22. 22.Is 6947 divisible by 7?
  23. 23.Is 121642 divisible by 19?
  24. 24.Is 19968 divisible by 3?
  25. 25.Is 13304 divisible by 4?
  26. 26.Is 119690 divisible by 18?
  27. 27.Is 1010 divisible by 2?
  28. 28.Is 23602 divisible by 7?
  29. 29.Is 9979 divisible by 2?
  30. 30.Is 79599 divisible by 13?
  31. 31.Is 14693 divisible by 9?
  32. 32.Is 13230 divisible by 6?
  33. 33.Is 3386 divisible by 4?
  34. 34.Is 22380 divisible by 6?
  35. 35.Is 75440 divisible by 18?
  36. 36.Is 48668 divisible by 23?
  37. 37.Is 28146 divisible by 7?
  38. 38.Is 36643 divisible by 8?
  39. 39.Is 94618 divisible by 15?
  40. 40.Is 15584 divisible by 11?

Answer key

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

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