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.

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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).

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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

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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

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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.