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Answers for “如何检查质因数分解是否正确?”

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Understand why

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Numbers in the factor tree are circled to indicate that they are prime numbers, which serve as terminal leaves and cannot be broken down further in this procedure.

Conditions: A branch is continued only if the current number is composite.; A branch stops once the current number is prime.

Understand why

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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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You stop breaking down a factor once it is prime because prime numbers only have two factors, 1 and the number itself, meaning they cannot be broken down further into smaller positive integers.

Conditions: The current branch value is prime.; The goal is to express the original number as a product of primes only.