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Prime Factorization

Đối tượng: Middle SchoolThể loại: Math

Mô tả

Animates factor trees for 60 and 84, showing how any composite number can be broken down into a unique product of prime numbers. Prime numbers are highlighted in distinct colors and the final exponential form is displayed with MathTex.

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Prime Factorization

Description

Animates factor trees for 60 and 84, showing how any composite number can be broken down into a unique product of prime numbers. Prime numbers are highlighted in distinct colors and the final exponential form is displayed with MathTex.

Phases

# Phase Name Duration Description
1 What is a Prime? 5s Briefly show first few primes: 2, 3, 5, 7, 11 highlighted in color.
2 Factor Tree for 60 14s Start with 60, branch to 6×10, then 2×3 and 2×5. Highlight prime leaves.
3 Write 60 in Prime Form 6s Display 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5 using MathTex.
4 Factor Tree for 84 12s Start with 84, branch to 4×21, then 2×2 and 3×7. Highlight primes.
5 Write 84 in Prime Form 5s Display 84 = 2² × 3 × 7 using MathTex.
6 Summary 4s Every number has a unique prime factorization (Fundamental Theorem).

Layout

+------------------------------------------------------+
|     [Title: Prime Factorization]                     |
|                                                      |
|   [Tree for 60]           [Tree for 84]              |
|       60                       84                    |
|      /  \                    /    \                  |
|     6    10                 4      21                |
|    / \  / \               / \    /  \                |
|   2   3 2   5            2   2  3    7               |
|                                                      |
|  [Prime form formulas below each tree]               |
+------------------------------------------------------+

Area Descriptions

Area Content Notes
Top Title Persistent
Left Factor tree for 60 Sequential animation
Right Factor tree for 84 Sequential animation
Bottom Prime form MathTex Per tree

Assets & Dependencies

  • Fonts: LaTeX / sans-serif
  • Colors:
    • 2: RED
    • 3: BLUE
    • 5: GREEN
    • 7: ORANGE
    • Composite numbers: WHITE / LIGHT_GRAY
    • Branch lines: GRAY
    • Background: #1a1a2e
  • Manim version: ManimCE 0.19.1

Notes

  • Nodes are Text/MathTex objects positioned manually.
  • Lines connect parent node to children (Line objects animated with Create).
  • Prime leaves get a colored Circle highlight around them.
  • Both trees are shown sequentially (not simultaneously) for clarity.