What is the largest natural number \(N \) such that we can NOT subdivide an equilateral triangle into \(N\), not necessarily congruent, equilateral triangles?

Examples:

- We CAN subdivide an equilateral triangle into 4 equilateral triangles like in the image above.
- But we can NOT subdivide an equilateral triangle into 2 (possibly different) equilateral triangles.

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