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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 613 · 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 90207 divisible by 13?
  2. 2.Is 24240 divisible by 10?
  3. 3.Is 23523 divisible by 4?
  4. 4.Is 143640 divisible by 24?
  5. 5.Is 69866 divisible by 29?
  6. 6.Is 49428 divisible by 9?
  7. 7.Is 22696 divisible by 4?
  8. 8.Is 96921 divisible by 30?
  9. 9.Is 47815 divisible by 23?
  10. 10.Is 31031 divisible by 11?
  11. 11.Is 14060 divisible by 18?
  12. 12.Is 16420 divisible by 20?
  13. 13.Is 206400 divisible by 30?
  14. 14.Is 77444 divisible by 18?
  15. 15.Is 9548 divisible by 2?
  16. 16.Is 25169 divisible by 20?
  17. 17.Is 74160 divisible by 24?
  18. 18.Is 18428 divisible by 17?
  19. 19.Is 5756 divisible by 7?
  20. 20.Is 2378 divisible by 29?
  21. 21.Is 3290 divisible by 7?
  22. 22.Is 9898 divisible by 29?
  23. 23.Is 8126 divisible by 17?
  24. 24.Is 27336 divisible by 24?
  25. 25.Is 5866 divisible by 15?
  26. 26.Is 92531 divisible by 17?
  27. 27.Is 136482 divisible by 23?
  28. 28.Is 7053 divisible by 3?
  29. 29.Is 1193 divisible by 11?
  30. 30.Is 9947 divisible by 7?
  31. 31.Is 18456 divisible by 24?
  32. 32.Is 5850 divisible by 2?
  33. 33.Is 101130 divisible by 15?
  34. 34.Is 139830 divisible by 30?
  35. 35.Is 59534 divisible by 17?
  36. 36.Is 3622 divisible by 4?
  37. 37.Is 35835 divisible by 29?
  38. 38.Is 40860 divisible by 9?
  39. 39.Is 23272 divisible by 4?
  40. 40.Is 2033 divisible by 2?

Answer key

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

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