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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 119 · 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 38188 divisible by 7?
  2. 2.Is 23984 divisible by 8?
  3. 3.Is 55730 divisible by 10?
  4. 4.Is 15209 divisible by 3?
  5. 5.Is 13679 divisible by 10?
  6. 6.Is 86457 divisible by 13?
  7. 7.Is 12531 divisible by 3?
  8. 8.Is 118035 divisible by 20?
  9. 9.Is 11319 divisible by 13?
  10. 10.Is 13929 divisible by 4?
  11. 11.Is 38553 divisible by 30?
  12. 12.Is 10396 divisible by 5?
  13. 13.Is 81170 divisible by 17?
  14. 14.Is 24070 divisible by 6?
  15. 15.Is 14025 divisible by 11?
  16. 16.Is 36266 divisible by 7?
  17. 17.Is 325 divisible by 2?
  18. 18.Is 56606 divisible by 11?
  19. 19.Is 1967 divisible by 2?
  20. 20.Is 16862 divisible by 3?
  21. 21.Is 23124 divisible by 6?
  22. 22.Is 18076 divisible by 11?
  23. 23.Is 5642 divisible by 7?
  24. 24.Is 62251 divisible by 9?
  25. 25.Is 47511 divisible by 9?
  26. 26.Is 2596 divisible by 3?
  27. 27.Is 1750 divisible by 19?
  28. 28.Is 6564 divisible by 29?
  29. 29.Is 8445 divisible by 2?
  30. 30.Is 38028 divisible by 6?
  31. 31.Is 16774 divisible by 5?
  32. 32.Is 113940 divisible by 20?
  33. 33.Is 62982 divisible by 9?
  34. 34.Is 18487 divisible by 30?
  35. 35.Is 74190 divisible by 15?
  36. 36.Is 15160 divisible by 29?
  37. 37.Is 58084 divisible by 13?
  38. 38.Is 14588 divisible by 3?
  39. 39.Is 12922 divisible by 7?
  40. 40.Is 27137 divisible by 11?

Answer key

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

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