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Factorization - Exploring Divisor Pairs

Factorization - Exploring Divisor Pairs
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2020-01-27 21:59
FunctionCoordinate GeometryGeometric Construction
This example allows you to input an integer and explore different ways to generate it based on its prime factorization. Key mathematical concepts include factorization and divisors. GeoGebra commands such as Factors, Join, and Sequence are used in its construction. Suitable for middle school and above students to learn about factorization and number theory.

GeoGebra Commands & Parameters

  1. Factors(n) → fm
  2. Join(Sequence[Sequence[Element[Element[fm, i], 1], j, 1, Element[Element[fm, i], 2]], i, 1, Length[fm]]) → factors
  3. Sequence(If[Element[bools, i] ∧ Length[factors] ≥ i, Element[factors, i], 1], i, 1, Length[bools]) → list1
  4. Sequence(((floor(i / prows) * d), (Mod[i, prows] * d)) + (ts * Vector[((floor(i / prows) * d), (Mod[i, prows] * d)), (((floor(i / rows) * d), Mod[i, rows]) * d)]), i, 0, n - 1) → points
  5. Element(points, n) → MX
  6. Textfield(n) → inputBox1
  7. Sequence(If[(¬Element[bools, i]) ∧ Length[factors] ≥ i, Element[factors, i], 1], i, 1, Length[bools]) → list2
  8. Min(Sequence[If[Element[bools, i], i, 10000], i, 1, Length[bools]]) → minTrue
  9. Min(Sequence[If[¬Element[bools, i], i, 10000], i, 1, Length[bools]]) → minFalse
  10. Sequence(If[i ≤ Length[factors] ∧ Element[bools, i], If[i > minTrue, "\times", ""] + (Element[list1, i]), ""], i, 1, Length[bools]) → rt
  11. Sequence(If[i ≤ Length[factors] ∧ (¬Element[bools, i]), If[i > minFalse, "\times", ""] + (Element[list2, i]), ""], i, 1, Length[bools]) → ct
  12. Corner(5) → GV
  13. Max(Sequence[If[¬Element[bools, i], i, 0], i, 1, Min[Length[bools], Length[factors]]]) → maxFalse
  14. Max(Sequence[If[Element[bools, i], i, 0], i, 1, Min[Length[bools], Length[factors]]]) → maxTrue
  15. Sequence(Circle[Element[points, i], (0.3 * d)], i, 1, n) → list3
  16. If(MXratio > ratio, innerW / ratio, innerH) → finH
  17. If(MXratio > ratio, innerW, (innerH * ratio)) → finW
  18. Text(If[rows ≟ 1, "1", Element[rt, 1] + (Element[rt, 2]) + (Element[rt, 3]) + (Element[rt, 4]) + (Element[rt, 5]) + (Element[rt, 6]) + (Element[rt, 7]) + (If[minTrue ≟ maxTrue, "", "=" + rows])], RT, false, true) → text1
  19. Text(If[cols ≟ 1, "1", Element[ct, 1] + (Element[ct, 2]) + (Element[ct, 3]) + (Element[ct, 4]) + (Element[ct, 5]) + (Element[ct, 6]) + (Element[ct, 7]) + (If[minFalse ≟ maxFalse, "", "=" + cols])], CT, false, true) → text2
  20. Sequence(If[Element[bools, i], "darkgreen", "red"], i, 1, Length[bools]) → colors

AI Drawing Prompt Reference

Create a visualization of the prime factorization of an integer. Start by entering an integer, then display its prime factors. Use these factors to generate different factor pairs and represent them with points. Finally, generate two product expressions based on these factor pairs, one showing the product of correct pairs and the other showing the product of incorrect pairs.
The prompt above was compiled from the original drawing commands and is for reference only.