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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 835 · 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 48680 divisible by 8?
  2. 2.Is 4275 divisible by 5?
  3. 3.Is 1301 divisible by 2?
  4. 4.Is 35574 divisible by 23?
  5. 5.Is 16587 divisible by 19?
  6. 6.Is 138966 divisible by 30?
  7. 7.Is 168606 divisible by 29?
  8. 8.Is 12472 divisible by 9?
  9. 9.Is 65790 divisible by 15?
  10. 10.Is 9720 divisible by 2?
  11. 11.Is 18935 divisible by 3?
  12. 12.Is 4410 divisible by 10?
  13. 13.Is 22943 divisible by 4?
  14. 14.Is 9173 divisible by 5?
  15. 15.Is 19926 divisible by 4?
  16. 16.Is 91705 divisible by 29?
  17. 17.Is 4249 divisible by 17?
  18. 18.Is 24200 divisible by 4?
  19. 19.Is 9355 divisible by 2?
  20. 20.Is 72505 divisible by 13?
  21. 21.Is 11863 divisible by 3?
  22. 22.Is 22223 divisible by 10?
  23. 23.Is 147736 divisible by 30?
  24. 24.Is 15447 divisible by 3?
  25. 25.Is 9045 divisible by 5?
  26. 26.Is 73293 divisible by 13?
  27. 27.Is 18696 divisible by 19?
  28. 28.Is 9378 divisible by 4?
  29. 29.Is 9071 divisible by 7?
  30. 30.Is 147813 divisible by 29?
  31. 31.Is 2446 divisible by 6?
  32. 32.Is 13036 divisible by 3?
  33. 33.Is 10005 divisible by 9?
  34. 34.Is 45324 divisible by 18?
  35. 35.Is 18897 divisible by 6?
  36. 36.Is 3758 divisible by 4?
  37. 37.Is 54840 divisible by 12?
  38. 38.Is 2088 divisible by 24?
  39. 39.Is 45750 divisible by 10?
  40. 40.Is 21540 divisible by 30?

Answer key

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

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