How do you use a factor tree to find prime factors?

Conditions

• Used for factoring composite numbers.
• Each parent node must equal the product of its two child factors.
• Composite branches must be split again.
• Prime branches are terminal and are circled in this lesson.

Reasoning, step by step

1. Start with the target number at the top of the tree.
2. Choose any two factors whose product is that number and write them below as branches.
3. Repeat the process on each composite branch.
4. Stop when every remaining leaf is a prime number.
5. Collect the prime leaves to write the final product.

Example

To factor 30, you can branch it into 2 and 15. Since 15 is composite, branch it into 3 and 5. The leaves are 2, 3, and 5, which are all prime, so the factorization is $30 = 2 \times 3 \times 5$.

Common misconceptions

• Stopping as soon as a number is split into two factors and treating that as the final prime factorization.
• Believing that choosing a different first factor pair changes the final prime factors.

Watch the explanation

Explore next

• Why are some numbers in the factor tree circled?
• If I start a factor tree with a different pair of factors, will I get the same prime factors?