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Prime Factorization of Positive Integers by Alex CHIK

Prime Factorization of Positive Integers by Alex CHIK
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2020-01-31 16:14
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This example demonstrates the process of prime factorization for positive integers. Key math concepts include prime numbers, factors, and the fundamental theorem of arithmetic. GeoGebra commands and objects used in the construction are PrimeFactors, Append, Zip, Sequence, Textfield, TableText, Factors, Unique, LaTeX, and IsPrime. Suitable for middle school and above students to understand and practice prime factorization.

GeoGebra Commands & Parameters

  1. PrimeFactors(a) → list1
  2. Append(1, Sequence[Product[list1, k], k, 1, Length[list1]]) → list1P
  3. Zip(a / k, k, list1P) → listA
  4. Sequence(Append[First[list1, i], listA(i + 1)], i, 1, Length[listA] - 2) → listM1
  5. Append(listM1, list1) → listM2
  6. Textfield(a) → InputBox1
  7. TableText({First[listA, step + 1]}, "|100 _01vr") → text1
  8. Factors(a) → M1
  9. Unique(PrimeFactors[a]) → listUniqueFactors
  10. Append(Zip[Text[p] + (UnicodeToLetter[8901]), p, Take[listM3, 1, Length[listM3] - 1]], Text[Element[listM3, Length[listM3]]]) → listFactorText
  11. Zip(((Element[p, 1] * If[Element[p, 2] ≠ 1, (("^{" * Element[p, 2]) * "}")]) * If[{p} ≠ Last[M1], UnicodeToLetter[8901], ""]), p, M1) → listTextA
  12. LaTeX("=" + (Sum[listFactorText])) → text3
  13. IsPrime(a) → prime
  14. TableText({First[list1, step]}, "rv") → text2
  15. LaTeX("=\underline\underline{" + (Sum[listTextA]) + "}") → textA

AI Drawing Prompt Reference

Create an interactive diagram for demonstrating prime factorization of positive integers. It includes an input box for entering a positive integer. Below, a table shows the factorization steps: the first row lists the current divisor, and the second row shows the corresponding quotient. The final factorization is displayed as a mathematical expression, e.g., "12 = 2 × 2 × 3", with repeated primes written using exponents like "2^2 × 3". If the input is prime, it is highlighted. The diagram clearly shows intermediate steps and the final result, suitable for middle school students.
The prompt above was compiled from the original drawing commands and is for reference only.