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Express Composite Numbers as Product of Prime Numbers

Express Composite Numbers as Product of Prime Numbers
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2022-12-27 23:09
Geometric Construction
This example demonstrates how composite numbers can be expressed as products of prime numbers, highlighting the fundamental role of primes in multiplication. The key mathematical concepts involve prime factorization and number decomposition. Construction uses GeoGebra commands such as PrimeFactors, IsPrime, and Sequence to visualize the factorization process. Suitable for students in grades 4-5 to reinforce number sense and factorization skills.

GeoGebra Commands & Parameters

  1. KeepIf(Mod[selectedNum, jj] ≟ 0, jj, Sequence[selectedNum]) → factorsAll
  2. If(¬Defined[selectedNum], {}, If[active1, {"$\math{1 \times 1 }\;$"}, Zip[(((("$\math{" * Text[kk]) * " \times ") * Text[selectedNum / kk]) * "\; }$"), kk, factorsAll]]) → dropDown
  3. SelectedIndex(dropDown) → Options
  4. If(Length[selectedNums] ≤ 1, {1}, Take[selectedNums, 1, Length[selectedNums] - 1]) → selectedNums'
  5. If(countQuestion ≤ 30, Product[Take[selectedNums, 1, Length[selectedNums] - 1]], Element[factorsAll, Options]) → firstFact
  6. Sequence("×", kk, 1, Length[selectedNums] - 1) → times
  7. Flatten({Sequence[{Element[selectedNums', kk], Element[times, kk]}, kk, 1, Length[times] - 1], Last[selectedNums']}) → product'
  8. If(countQuestion ≤ 30, TableText[Flatten[RemoveUndefined[{If[Length[selectedNums'] ≥ 2, product', Length[selectedNums'] ≟ 1, Last[selectedNums'], {}], If[Length[selectedNums'] ≥ 2, "="], If[Length[selectedNums'] ≥ 2, Text[Product[selectedNums']]]}]], "lh"], Text[Element[factorsAll, Options]]) → ProductText'
  9. Corner(5) → AppSize
  10. Flatten(Sequence[Sequence[(kk * horizontalSeparation), kk, 1, 30 / rows], jj, 1, rows]) → xCoordinates
  11. Flatten(Sequence[Sequence[8.4 - (anim * 0.5) - (kk * verticalSeparation), jj, 1, 30 / rows], kk, 0, rows]) → yCoordinates
  12. Zip((jj, kk), jj, xCoordinates, kk, yCoordinates) → textsPositions
  13. Text((("\ovalbox{" * A10) * "}"), Element[textsPositions, A10], true, true, 0, 0) → B10
  14. Text((("\ovalbox{" * A11) * "}"), Element[textsPositions, A11], true, true, 0, 0) → B11
  15. Text((("\ovalbox{" * A12) * "}"), Element[textsPositions, A12], true, true, 0, 0) → B12
  16. Text((("\ovalbox{" * A13) * "}"), Element[textsPositions, A13], true, true, 0, 0) → B13
  17. Text((("\ovalbox{" * A14) * "}"), Element[textsPositions, A14], true, true, 0, 0) → B14
  18. Text((("\ovalbox{" * A15) * "}"), Element[textsPositions, A15], true, true, 0, 0) → B15
  19. Text((("\ovalbox{" * A16) * "}"), Element[textsPositions, A16], true, true, 0, 0) → B16
  20. Text((("\ovalbox{" * A17) * "}"), Element[textsPositions, A17], true, true, 0, 0) → B17
  21. Text((("\ovalbox{" * A18) * "}"), Element[textsPositions, A18], true, true, 0, 0) → B18
  22. Text((("\ovalbox{" * A19) * "}"), Element[textsPositions, A19], true, true, 0, 0) → B19
  23. Text((("\ovalbox{" * A20) * "}"), Element[textsPositions, A20], true, true, 0, 0) → B20
  24. Text((("\ovalbox{" * A21) * "}"), Element[textsPositions, A21], true, true, 0, 0) → B21
  25. Text((("\ovalbox{" * A22) * "}"), Element[textsPositions, A22], true, true, 0, 0) → B22
  26. Text((("\ovalbox{" * A23) * "}"), Element[textsPositions, A23], true, true, 0, 0) → B23
  27. Text((("\ovalbox{" * A24) * "}"), Element[textsPositions, A24], true, true, 0, 0) → B24
  28. Text((("\ovalbox{" * A25) * "}"), Element[textsPositions, A25], true, true, 0, 0) → B25
  29. Text((("\ovalbox{" * A26) * "}"), Element[textsPositions, A26], true, true, 0, 0) → B26
  30. Text((("\ovalbox{" * A27) * "}"), Element[textsPositions, A27], true, true, 0, 0) → B27
  31. Text((("\ovalbox{" * A28) * "}"), Element[textsPositions, A28], true, true, 0, 0) → B28
  32. Text((("\ovalbox{" * A29) * "}"), Element[textsPositions, A29], true, true, 0, 0) → B29
  33. Text((("\ovalbox{" * A30) * "}"), Element[textsPositions, A30], true, true, 0, 0) → B30
  34. IsPrime(A1) → C1
  35. IsPrime(A2) → C2
  36. IsPrime(A3) → C3
  37. IsPrime(A4) → C4
  38. IsPrime(A5) → C5
  39. IsPrime(A6) → C6
  40. IsPrime(A7) → C7
  41. IsPrime(A8) → C8
  42. IsPrime(A9) → C9
  43. IsPrime(A10) → C10
  44. IsPrime(A11) → C11
  45. IsPrime(A12) → C12
  46. IsPrime(A13) → C13
  47. IsPrime(A14) → C14
  48. IsPrime(A15) → C15
  49. IsPrime(A16) → C16
  50. IsPrime(A17) → C17
  51. IsPrime(A18) → C18
  52. IsPrime(A19) → C19
  53. IsPrime(A20) → C20
  54. IsPrime(A21) → C21
  55. IsPrime(A22) → C22
  56. IsPrime(A23) → C23
  57. IsPrime(A24) → C24
  58. IsPrime(A25) → C25
  59. IsPrime(A26) → C26
  60. IsPrime(A27) → C27
  61. IsPrime(A28) → C28
  62. IsPrime(A29) → C29
  63. IsPrime(A30) → C30
  64. Zip((((("SetFixed(B" * jj) * ",true, ") * If[kk, "true", "false"]) * ")"), jj, Sequence[30], kk, primesOrNot) → FixNonPrimes
  65. Flatten({Sequence[{Element[selectedNums, kk], Element[times, kk]}, kk, 1, Length[times]], Last[selectedNums]}) → product
  66. Text((("\ovalbox{\hspace{4}" * A1) * "\hspace{5}}"), Element[textsPositions, A1], true, true, 0, 0) → B1
  67. Text((("\ovalbox{\hspace{4}" * A2) * "\hspace{5}}"), Element[textsPositions, A2], true, true, 0, 0) → B2
  68. Text((("\ovalbox{\hspace{4}" * A3) * "\hspace{5}}"), Element[textsPositions, A3], true, true, 0, 0) → B3
  69. Text((("\ovalbox{\hspace{4}" * A4) * "\hspace{5}}"), Element[textsPositions, A4], true, true, 0, 0) → B4
  70. Text((("\ovalbox{\hspace{4}" * A5) * "\hspace{5}}"), Element[textsPositions, A5], true, true, 0, 0) → B5
  71. Text((("\ovalbox{\hspace{4}" * A6) * "\hspace{5}}"), Element[textsPositions, A6], true, true, 0, 0) → B6
  72. Text((("\ovalbox{\hspace{4}" * A7) * "\hspace{5}}"), Element[textsPositions, A7], true, true, 0, 0) → B7
  73. Text((("\ovalbox{\hspace{4}" * A8) * "\hspace{5}}"), Element[textsPositions, A8], true, true, 0, 0) → B8
  74. Text((("\ovalbox{\hspace{4}" * A9) * "\hspace{5}}"), Element[textsPositions, A9], true, true, 0, 0) → B9
  75. If(countQuestion ≤ 30, selectedNums(Length[selectedNums]), selectedNum / Element[factorsAll, Options]) → secondFact
  76. Min(RemoveUndefined[{1, 3.2 / secondFact, 14 / firstFact}]) → sqLength
  77. If(Length[selectedNums] ≥ 2, Sequence[Translate[B, ((0, (-sqLength)) * kk)], kk, 0, secondFact], {(-10, 0), (-10, -10)}) → PointsLeft
  78. If(Length[selectedNums] ≥ 2, Sequence[Translate[B, ((sqLength, 0) * kk)], kk, 0, firstFact], {(-10, 0), (-10, -10)}) → PointsUp
  79. Translate(PointsLeft, (If[Length[selectedNums] ≥ 2, (sqLength * firstFact), 1], 0)) → PointsRight
  80. Translate(PointsUp, Vector[(0, ((-If[Length[selectedNums] ≥ 2, secondFact, 1]) * sqLength))]) → PointsDown
  81. Polygon({Element[PointsDown, 1], Element[PointsDown, Length[PointsDown]], Element[PointsRight, 1], B}) → q1
  82. Text(secondFact) → labelVSegment
  83. If(Length[selectedNums] ≥ 2, Text[labelVSegment, Midpoint[vSegment], true, true, 1, 0], "") → labelVPositioned_{1}
  84. If(Length[selectedNums] ≥ 2, Text[labelHSegment, Midpoint[hSegment], true, true, 0, -1], "") → labelHPositioned
  85. Sequence((((("SetConditionToShowObject(B" * jj) * ", D") * jj) * ")"), jj, 4, 30) → conditionalVisibForTexts
  86. PrimeFactors(countQuestion) → l1
  87. If(prime ∧ IsPrime[countQuestion], "That's correct!", prime ∧ (¬IsPrime[countQuestion]), ((("Notice that " * l1(1)) * " is a factor of ") * countQuestion), (¬prime) ∧ Product[selectedNums] ≟ countQuestion, "Well done!", (("The product is not equal to " * countQuestion) * ". Keep trying.")) → feedbackText
  88. Translate(B, (0, -5)) → B'
  89. Zip(Segment[AA, BB], AA, PointsLeft, BB, PointsRight) → segmentsH
  90. Zip(Segment[AA, BB], AA, PointsUp, BB, PointsDown) → segmentsV
  91. Translate(PointsRight(1), (0.5, 0)) → A
  92. Translate(PointsRight(Length[PointsRight]), (0.5, 0)) → C
  93. Segment(A, C) → f
  94. Text(("\hspace{5}" * labelVSegment), Midpoint[f], true, true, 1, 0) → labelVPositioned
  95. Translate(PointsLeft(Length[PointsLeft]), (0, -0.5)) → D
  96. Translate(PointsRight(Length[PointsRight]), (0, -0.5)) → E
  97. Segment(D, E) → g
  98. Text(ProductText', Midpoint[g], true, true, 0, -1) → labelHPositoned
  99. TableText(Flatten[{If[Length[selectedNums] ≥ 2, product, Length[selectedNums] ≟ 1, Last[selectedNums], {}], If[Length[selectedNums] ≥ 2, "=", ""], If[Length[selectedNums] ≥ 2, Text[Product[selectedNums]], ""]}], "lh") → ProductText
  100. Polygon(Element[PointsRight, 1], Element[PointsLeft, 1], 4) → poly1
  101. Segment(Translate[PointsLeft(1), (0, -1.5)], Translate[PointsRight(1), (0, -1.5)]) → h
  102. Segment(Translate[PointsRight(1), (0.5, 0)], Translate[PointsRight(1), (0.5, -1)]) → i
  103. Zip((("SetFixed(B" * jj) * ",true, true)"), jj, Sequence[30]) → UnFixAll
  104. Corner(ProductText, 3) → PosUnDo
  105. Text(feedback, B', true, true, 1, 0) → feedbackTextPositioned
  106. Translate(hGuideLine, Vector[(Vector[Corner[4], Corner[1]] / 500 * 16)]) → hGuideLine'
  107. Zip((((("SetColor(B" * jj) * ", ") * If[kk, "colorPrime", "colorInactive"]) * ")"), jj, Sequence[30], kk, primesOrNot) → ColorTheNumbers
  108. Text(ProductText', (0, y(Midpoint[g])), true, true, 1, -1) → labelHPositioned2
  109. Corner(labelHPositoned, 1) → CorLabelH
  110. Zip((((("SetColor(B" * jj) * ", ") * If[jj ≟ 1, "colorBlack", If[kk, "colorPrime", "colorNonPrime"]]) * ")"), jj, Sequence[30], kk, primesOrNot) → ColorTheNumbers2

AI Drawing Prompt Reference

Visualize how a composite number can be expressed as a product of prime numbers, emphasizing the fundamental role of primes in multiplication. Select a composite number, then decompose it into a sequence of prime factors and display them connected by multiplication signs to form an expression. Highlight each prime factor with circles and arrange them in order to clearly show the prime factorization process.
The prompt above was compiled from the original drawing commands and is for reference only.