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HCF and LCM of Two Numbers by Short Division

HCF and LCM of Two Numbers by Short Division
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2015-05-24 09:22
FunctionGeometric Construction
This example demonstrates how to find the highest common factor (HCF) and least common multiple (LCM) of two numbers using the short division method. Key mathematical concepts include the theory of HCF and LCM. Using GeoGebra commands such as PrimeFactors, Append, and Zip, the process is visually illustrated. Suitable for students from upper elementary to middle school.

GeoGebra Commands & Parameters

  1. PrimeFactors(GCD[{a, b}]) → list1
  2. Append(1, Sequence[Product[list1, k], k, 1, Length[list1]]) → list1P
  3. Zip(a / k, k, list1P) → listA
  4. Zip(b / k, k, list1P) → listB
  5. Element(Last[listA], 1) → a'
  6. Element(Last[listB], 1) → b'
  7. Textfield(a) → inputBox1
  8. Textfield(b) → inputBox2
  9. Append(Zip[Text[p] + (UnicodeToLetter[8901]), p, Take[list1, 1, Length[list1] - 1]], Text[Element[list1, Length[list1]]]) → listTextHCF
  10. Join({list1, Last[listA], Last[listB]}) → listLCM
  11. Append(Zip[Text[p] + (UnicodeToLetter[8901]), p, Take[listLCM, 1, Length[listLCM] - 1]], Text[Element[listLCM, Length[listLCM]]]) → listTextLCM
  12. TableText({First[listA, step1 + 1], First[listB, step1 + 1]}, "|100 _01vr") → text1
  13. TableText({First[list1, step1]}, "vr") → text4