Why are some numbers in the factor tree circled?

Conditions

• A branch is continued only if the current number is composite.
• A branch stops once the current number is prime.

Reasoning, step by step

1. Identify whether the current number in the branch is prime or composite.
2. If it is prime, circle it to mark the end of that branch.
3. If it is composite, continue to break it down into smaller factors.

Example

In the factor tree for 30, the numbers 2, 3, and 5 are circled because they are prime, while 15 is not circled because it is composite and must be broken down into 3 and 5.

Common misconceptions

• Thinking that an intermediate factorization is complete; composite branches such as 15 must be broken down further until every leaf is prime.

Watch the explanation

Explore next

• Why do you stop breaking down a factor once it is prime?
• How can you check that a prime factorization is correct?