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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 140 · 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 72520 divisible by 20?
  2. 2.Is 115408 divisible by 19?
  3. 3.Is 21442 divisible by 23?
  4. 4.Is 34584 divisible by 6?
  5. 5.Is 79579 divisible by 12?
  6. 6.Is 33335 divisible by 18?
  7. 7.Is 5100 divisible by 3?
  8. 8.Is 36145 divisible by 9?
  9. 9.Is 6732 divisible by 12?
  10. 10.Is 94845 divisible by 15?
  11. 11.Is 66474 divisible by 18?
  12. 12.Is 49330 divisible by 10?
  13. 13.Is 73428 divisible by 29?
  14. 14.Is 20128 divisible by 4?
  15. 15.Is 16761 divisible by 5?
  16. 16.Is 4897 divisible by 3?
  17. 17.Is 5516 divisible by 7?
  18. 18.Is 152940 divisible by 30?
  19. 19.Is 17810 divisible by 7?
  20. 20.Is 33315 divisible by 8?
  21. 21.Is 3725 divisible by 4?
  22. 22.Is 27300 divisible by 5?
  23. 23.Is 68092 divisible by 29?
  24. 24.Is 519 divisible by 2?
  25. 25.Is 8729 divisible by 29?
  26. 26.Is 12590 divisible by 8?
  27. 27.Is 74594 divisible by 13?
  28. 28.Is 8555 divisible by 17?
  29. 29.Is 24561 divisible by 9?
  30. 30.Is 24150 divisible by 5?
  31. 31.Is 17911 divisible by 15?
  32. 32.Is 53610 divisible by 17?
  33. 33.Is 94220 divisible by 20?
  34. 34.Is 31140 divisible by 5?
  35. 35.Is 2975 divisible by 5?
  36. 36.Is 34120 divisible by 15?
  37. 37.Is 131518 divisible by 23?
  38. 38.Is 1145 divisible by 3?
  39. 39.Is 76355 divisible by 17?
  40. 40.Is 175230 divisible by 30?

Answer key

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

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