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Prime Factorization with Tree Diagrams

Prime Factorization with Tree Diagrams
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2020-12-13 19:26
FunctionCalculusGeometric ConstructionSlider Animation
This example demonstrates prime factorization using tree diagrams. It involves core math concepts like prime factorization, tree diagrams, and algebraic operations. The construction uses GeoGebra commands such as Factors, Join, Vector, Textfield, Sequence, Mirror, IsPrime, and Text. It is suitable for middle school students and above learning prime factorization and algebra basics, or for educational demonstrations.

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. Vector(VVP) → vu
  4. Textfield(n) → inputBox1
  5. Vector(VP) → u
  6. Sequence(ANC + (i * u), i, 0, Length[factors] - 1) → list2
  7. Sequence(Product[Sequence[Element[factors, j], j, i, Length[factors]]], i, 1, Length[factors]) → list1
  8. Mirror(u, x = 0) → u2
  9. Sequence(Element[list2, i] + u2, i, 1, Length[list2] - 1) → list3
  10. Sequence(Text["\" + (If[i ≟ Length[list1], "red", "blue"]) + "{" + (Element[list1, i]) + "}", Element[list2, i], false, true], i, 1, len) → list4
  11. Sequence(Text["\red{" + (Element[factors, i]) + "}", Element[list3, i], false, true], i, 1, len - 1) → list5
  12. Sequence(Segment[Element[list2, i] + hv, Element[list2, i + 1]], i, 1, len - 1) → list6
  13. Sequence(Segment[Element[list2, i] + hvu, Element[list3, i] + wu], i, 1, len - 1) → list7
  14. Sequence(Text["\times", Element[list2, i] + vu, false, true], i, 1, len - 1) → list8
  15. IsPrime(n) → ip
  16. Text(If[ip, "\ Is\ Prime!", "=\red{" + (Sum[Sequence[If[i ≟ 1, "", "\times"] + (Element[factors, i]), i, 1, Length[factors]]]) + "}"], B, false, true) → text1

AI Drawing Prompt Reference

Draw a prime factorization tree diagram. Input a positive integer n, find all its prime factors, and then display these factors in a tree structure showing their multiplication relationships. Start from the root node and connect each factor node sequentially, finally showing the product expression of the factors.
The prompt above was compiled from the original drawing commands and is for reference only.