Factor Tree
A factor tree is a visual method for finding the prime factorization of a composite number. Start by splitting the number into any two factors, then continue splitting each non-prime factor until every branch ends in a prime number. For example, 54 splits into 6 and 9; 6 splits into 2 and 3; 9 splits into 3 and 3, giving the prime factorization 2 x 3 x 3 x 3. Factor trees are taught in Chapter 3 of Saxon Math Course 2 and are a foundational 7th grade math skill used for finding GCF, LCM, and simplifying fractions.
Key Concepts
Property A factor tree is a method to find the prime factorization of a number. Start by writing any two factors below the number. If a factor is not prime, continue breaking it down into two new factors until all the 'branches' of the tree end in prime numbers.
Examples To factor $54$, branch into $6$ and $9$. Then $6$ branches into $2$ and $3$, while $9$ branches into $3$ and $3$. The prime factors are $2, 3, 3, 3$. To factor $28$, branch into $4$ and $7$. The $7$ is prime, but the $4$ branches into $2$ and $2$. The prime factors are $2, 2, 7$.
Explanation Imagine a number is the trunk of a tree. It splits into two branches (factors). If a branch is composite, it splits again! You keep splitting the branches until they can’t split anymore, leaving you with the prime 'leaves' of the tree. These leaves, when multiplied together, give you the original trunk number. It's a visual way to decompose numbers.
Common Questions
What is a factor tree?
A factor tree is a diagram that breaks a composite number down into its prime factors by repeatedly splitting it into pairs of factors. The process continues until every branch ends with a prime number.
How do you make a factor tree for 28?
Start with 28 and split into 4 and 7. Since 7 is prime, it stays. Split 4 into 2 and 2. Both are prime, so the factor tree is complete: 28 = 2 x 2 x 7.
Does it matter which factors you start with in a factor tree?
No. You can start with any pair of factors and will always arrive at the same set of prime factors. This is guaranteed by the Fundamental Theorem of Arithmetic.
What is the difference between a factor tree and prime factorization?
A factor tree is the visual tool or diagram you use to find the prime factorization. Prime factorization is the final result: the number written as a product of only prime numbers.
Why are factor trees important in 7th grade math?
Factor trees help students find prime factorizations, which are needed for calculating the greatest common factor and least common multiple. These skills are essential for adding fractions with unlike denominators and simplifying ratios.
What are common mistakes when making factor trees?
Students sometimes stop branching too early by leaving a composite number like 4 or 9 as a final branch. Always check that every endpoint is a prime number before writing the factorization.