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Solution:

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There are different ways to fill in the missing numbers on the trees, but importantly one thing is always the same. The numbers you end up with on the bottoms of the branches are always the prime factors of the number at the top. Think about the 40 tree for example. We can make a 40 tree in many different ways:

Notice that any way we construct the branches, we end up with 5, 2, 2, 2 at the bottom. The fact that we always end up with the same prime numbers, no matter how we factor a number is so important that it is called The Fundamental Theorem of Arithmetic.

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