If I start a factor tree with a different pair of factors, will I get the same prime factors?

Conditions

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

Reasoning, step by step

1. Choose a different valid factor pair for the starting number.
2. Continue breaking down composite branches until all leaves are prime.
3. Compare the final prime leaves with those from another factor tree.

Example

For the number 30, starting with 2 and 15 leads to prime factors 2, 3, and 5. Starting with 5 and 6 also leads to prime factors 2, 3, and 5.

Common misconceptions

• Believing that choosing a different first factor pair changes the final prime factorization.
• Assuming that the order of the branches (left or right) affects the final result.

Watch the explanation

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