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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 242 · 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 116475 divisible by 30?
  2. 2.Is 24624 divisible by 12?
  3. 3.Is 8897 divisible by 7?
  4. 4.Is 124614 divisible by 23?
  5. 5.Is 121626 divisible by 29?
  6. 6.Is 68346 divisible by 19?
  7. 7.Is 10783 divisible by 3?
  8. 8.Is 71580 divisible by 12?
  9. 9.Is 28005 divisible by 18?
  10. 10.Is 26564 divisible by 7?
  11. 11.Is 33392 divisible by 15?
  12. 12.Is 3432 divisible by 12?
  13. 13.Is 123888 divisible by 29?
  14. 14.Is 26257 divisible by 11?
  15. 15.Is 87116 divisible by 15?
  16. 16.Is 15988 divisible by 7?
  17. 17.Is 7410 divisible by 15?
  18. 18.Is 16239 divisible by 3?
  19. 19.Is 37390 divisible by 10?
  20. 20.Is 75182 divisible by 15?
  21. 21.Is 15432 divisible by 3?
  22. 22.Is 32184 divisible by 24?
  23. 23.Is 82296 divisible by 18?
  24. 24.Is 48231 divisible by 23?
  25. 25.Is 10498 divisible by 18?
  26. 26.Is 27959 divisible by 7?
  27. 27.Is 5357 divisible by 5?
  28. 28.Is 38669 divisible by 12?
  29. 29.Is 4572 divisible by 9?
  30. 30.Is 18270 divisible by 7?
  31. 31.Is 54774 divisible by 10?
  32. 32.Is 101130 divisible by 15?
  33. 33.Is 4688 divisible by 12?
  34. 34.Is 54457 divisible by 24?
  35. 35.Is 6057 divisible by 2?
  36. 36.Is 12938 divisible by 8?
  37. 37.Is 106242 divisible by 17?
  38. 38.Is 1707 divisible by 2?
  39. 39.Is 57349 divisible by 15?
  40. 40.Is 17363 divisible by 4?

Answer key

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

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