Do you have to start a factor tree with 2 for an even number?

Conditions

• The number is even.
• The chosen first split is still a valid factor pair.

Reasoning, step by step

1. Identify that the number is even.
2. Recognize that 2 is a possible starting factor.
3. Choose another valid factor pair if desired.
4. Continue the factor tree until all leaves are prime.

Example

For the even number 48, the instructor starts with the factor pair 4 and 12 instead of 2 and 24, and still arrives at the correct prime factorization $48 = 2 \times 2 \times 2 \times 2 \times 3$.

Common misconceptions

• Thinking an even number's factor tree must begin with 2.
• Assuming that starting with a different factor pair will lead to a different prime factorization.

Watch the explanation

Explore next

• What is the prime factorization of 48?
• How can you check that a prime factorization is correct?