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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 553 · 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 34978 divisible by 30?
  2. 2.Is 15392 divisible by 18?
  3. 3.Is 5146 divisible by 5?
  4. 4.Is 1323 divisible by 3?
  5. 5.Is 21827 divisible by 23?
  6. 6.Is 7593 divisible by 2?
  7. 7.Is 54795 divisible by 30?
  8. 8.Is 4964 divisible by 4?
  9. 9.Is 31907 divisible by 9?
  10. 10.Is 27935 divisible by 19?
  11. 11.Is 161033 divisible by 29?
  12. 12.Is 13299 divisible by 2?
  13. 13.Is 191670 divisible by 30?
  14. 14.Is 17047 divisible by 10?
  15. 15.Is 85840 divisible by 23?
  16. 16.Is 86634 divisible by 18?
  17. 17.Is 33164 divisible by 20?
  18. 18.Is 3897 divisible by 2?
  19. 19.Is 12549 divisible by 3?
  20. 20.Is 22112 divisible by 8?
  21. 21.Is 469 divisible by 7?
  22. 22.Is 3042 divisible by 2?
  23. 23.Is 115038 divisible by 18?
  24. 24.Is 102984 divisible by 24?
  25. 25.Is 44840 divisible by 19?
  26. 26.Is 16815 divisible by 5?
  27. 27.Is 31896 divisible by 8?
  28. 28.Is 119427 divisible by 18?
  29. 29.Is 6902 divisible by 3?
  30. 30.Is 102504 divisible by 20?
  31. 31.Is 52016 divisible by 8?
  32. 32.Is 18180 divisible by 15?
  33. 33.Is 15374 divisible by 8?
  34. 34.Is 23176 divisible by 8?
  35. 35.Is 8141 divisible by 10?
  36. 36.Is 14282 divisible by 17?
  37. 37.Is 632 divisible by 8?
  38. 38.Is 139867 divisible by 29?
  39. 39.Is 75188 divisible by 19?
  40. 40.Is 73398 divisible by 12?

Answer key

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

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