Prime Factorization
Public: Middle SchoolCatégorie: Math
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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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.