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Factoring Numbers

Factoring Numbers
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2019-11-05 00:59
Probability & Statistics
This example demonstrates the graphical representation of the process of factoring numbers, involving core mathematical concepts like factors, prime factorization, and integer properties. It utilizes GeoGebra commands and objects such as Sequence, Sort, Join, RandomElement, PrimeFactors, Element, Length, Unique, If, DivisorsList, Factors, Remove, and Polygon to illustrate the concept. Suitable for middle school and above students to understand factorization and number theory.

GeoGebra Commands & Parameters

  1. Sequence(n, n, from, to) → lev1
  2. Sort(Join[{lev1, {21, 21, 21, 35, 35, 35, 23, 25, 27, 29, 49, 31, 23}}]) → lev2
  3. Join({Sequence[n, n, 2, 100], {121, 169}}) → lev5
  4. RandomElement(Element[lev, level]) → tal
  5. PrimeFactors(tal) → Lista_1
  6. Element(Lista_1, 1) → e1
  7. Element(Lista_1, 2) → e2
  8. Element(Lista_1, 3) → e3
  9. Element(Lista_1, 4) → e4
  10. Length(Lista_1) → l
  11. Element(Lista_1, 5) → e5
  12. Element(Lista_1, 6) → e6
  13. Unique(Sequence[NextPrime[n], n, 1, 96]) → l0
  14. If(tal ∈ l0, 0, If[tal ∈ l1, 1, If[tal ∈ l2, 2, If[tal ∈ l3, 3, If[tal ∈ l4, 4, 5]]]]) → c
  15. DivisorsList(tal) → Lista_2
  16. Factors(tal) →
  17. Remove(Lista_2, {1, tal}) → Lista_3
  18. If(jn ≟ 2 ∧ c ≟ 0 ∨ f11 > 1 ∧ f12 > 1 ∧ c ≟ 1 ∨ f21 > 1 ∧ f22 > 1 ∧ c ≟ 2 ∨ f31 > 1 ∧ f32 > 1 ∧ c ≟ 3 ∨ f41 > 1 ∧ f42 > 1 ∧ c ≟ 4 ∨ f51 > 1 ∧ f52 > 1 ∧ c ≟ 5, true, false) → klar
  19. Polygon({A, B, C, D}) → q1
  20. Polygon(E, F, G, H) → q2, e, f, g, h
  21. If(c > 1 ∧ f12 > 1 ∧ f21 ≟ 1, 8, If[c > 2 ∧ f22 > 1 ∧ f31 ≟ 1, 7, If[c > 3 ∧ f32 > 1 ∧ f41 ≟ 1, 6, If[c > 4 ∧ f42 > 1 ∧ f51 ≟ 1, 5, 20]]]) → koord
  22. Polygon({A1, B1, C1, D1}) → q3