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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 503 · 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 2257 divisible by 9?
  2. 2.Is 42249 divisible by 8?
  3. 3.Is 28458 divisible by 18?
  4. 4.Is 30103 divisible by 8?
  5. 5.Is 15742 divisible by 3?
  6. 6.Is 24902 divisible by 11?
  7. 7.Is 31378 divisible by 29?
  8. 8.Is 97672 divisible by 30?
  9. 9.Is 89142 divisible by 24?
  10. 10.Is 73918 divisible by 11?
  11. 11.Is 14488 divisible by 8?
  12. 12.Is 6669 divisible by 2?
  13. 13.Is 63404 divisible by 11?
  14. 14.Is 3741 divisible by 3?
  15. 15.Is 25239 divisible by 11?
  16. 16.Is 98190 divisible by 30?
  17. 17.Is 13111 divisible by 2?
  18. 18.Is 19812 divisible by 12?
  19. 19.Is 86567 divisible by 24?
  20. 20.Is 2885 divisible by 7?
  21. 21.Is 23900 divisible by 19?
  22. 22.Is 152554 divisible by 24?
  23. 23.Is 10724 divisible by 4?
  24. 24.Is 10780 divisible by 7?
  25. 25.Is 160830 divisible by 30?
  26. 26.Is 6492 divisible by 12?
  27. 27.Is 5431 divisible by 10?
  28. 28.Is 20743 divisible by 20?
  29. 29.Is 124950 divisible by 30?
  30. 30.Is 67800 divisible by 20?
  31. 31.Is 65142 divisible by 18?
  32. 32.Is 53269 divisible by 12?
  33. 33.Is 19331 divisible by 6?
  34. 34.Is 83185 divisible by 12?
  35. 35.Is 16392 divisible by 8?
  36. 36.Is 118098 divisible by 18?
  37. 37.Is 111059 divisible by 19?
  38. 38.Is 4212 divisible by 12?
  39. 39.Is 8795 divisible by 3?
  40. 40.Is 25736 divisible by 4?

Answer key

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

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