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HCF & LCM of Three Numbers by Short Division

HCF & LCM of Three Numbers by Short Division
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2020-08-18 20:51
This example demonstrates how to calculate the Highest Common Factor (HCF) and Least Common Multiple (LCM) of three numbers using the short division method via GeoGebra. Core mathematical concepts include divisibility, prime factorization, and number theory. Key GeoGebra commands and objects used are GCD, PrimeFactors, Append, Zip, Element, Join, Textfield, and TableText, which guide users through the step-by-step short division process and display results. Suitable for middle school and above students to grasp fundamental number theory concepts.

GeoGebra Commands & Parameters

  1. GCD({a, b, c}) → hcf
  2. PrimeFactors(GCD[{a, b, c}]) → list1
  3. Append(1, Sequence[Product[list1, k], k, 1, Length[list1]]) → list1P
  4. Zip(a / k, k, list1P) → listA
  5. Zip(b / k, k, list1P) → listB
  6. Zip(c / k, k, list1P) → listC
  7. Element(Last[listA], 1) → a'
  8. Element(Last[listB], 1) → b'
  9. Element(Last[listC], 1) → c'
  10. Join({PrimeFactors[GCD[a', b']], PrimeFactors[GCD[b', c']], PrimeFactors[GCD[c', a']]}) → list3
  11. Zip(If[Mod[a', k] ≟ 0, k, 1], k, list3) → list3a
  12. Textfield(a) → inputBox1
  13. Textfield(b) → inputBox2
  14. Textfield(c) → inputBox3
  15. Zip(If[Mod[b', k] ≟ 0, k, 1], k, list3) → list3b
  16. Zip(If[Mod[c', k] ≟ 0, k, 1], k, list3) → list3c
  17. Append(1, Sequence[Product[list3a, k], k, 1, Length[list3a]]) → list3aP
  18. Append(1, Sequence[Product[list3b, k], k, 1, Length[list3b]]) → list3bP
  19. Append(1, Sequence[Product[list3c, k], k, 1, Length[list3c]]) → list3cP
  20. Zip(a' / k, k, list3aP) → listA'
  21. Zip(b' / k, k, list3bP) → listB'
  22. Zip(c' / k, k, list3cP) → listC'
  23. Join({list1, list3, Last[listA'], Last[listB'], Last[listC']}) → listLCM
  24. Append(Zip[Text[p] + (UnicodeToLetter[8901]), p, Take[list1, 1, Length[list1] - 1]], Text[Element[list1, Length[list1]]]) → listTextHCF
  25. Append(Zip[Text[p] + (UnicodeToLetter[8901]), p, Take[listLCM, 1, Length[listLCM] - 1]], Text[Element[listLCM, Length[listLCM]]]) → listTextLCM
  26. TableText({First[listA, step1 + 1], First[listB, step1 + 1], First[listC, step1 + 1]}, "|10000 _01 vr") → text1
  27. TableText({First[listA', step2 + 1], First[listB', step2 + 1], First[listC', step2 + 1]}, "|10000 _01 vr") → text2
  28. TableText({First[list1, step1]}, "vr") → text1a
  29. TableText({First[list3, step2]}, "vr") → text2a

AI Drawing Prompt Reference

To draw a graphic that demonstrates the calculation of the Highest Common Factor (HCF) and Least Common Multiple (LCM) of three numbers using the short division method. The graphic should include three input numbers, the HCF, the LCM, prime factorizations, and the steps of the short division method. The construction order should be: first input the three numbers, then calculate the HCF and factorize it, next display the short division steps, and finally calculate the LCM and show the results.
The prompt above was compiled from the original drawing commands and is for reference only.