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Answers for “对于偶数,必须以 2 开始因数树吗?”

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No, you do not have to start a factor tree with 2 for an even number. While 2 is always a factor of an even number, you can choose any valid factor pair to begin the tree.

Conditions: The number is even.; The chosen first split is still a valid factor pair.

Understand why

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Yes, starting a factor tree with a different pair of factors will still yield the same prime factors. The final set of prime factors is unique regardless of the initial split.

Conditions: The number being factored is the same.; Each branch is decomposed into valid factor pairs.; The process continues until all leaves are prime.

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You can check a prime factorization by multiplying the prime factors back together. If the product equals the original number, the factorization is correct.

Conditions: The factors being multiplied must be the claimed prime factors.; The product must equal the original number exactly.