Factor Tree

Elementary SchoolMiddle School

Definition

One of the methods of carrying out prime factorization to identify prime factors of an integer. Prime factors are prime numbers that when multiplied, give you a number. In the factor tree method, each number branches off into into two numbers that will achieve the original number when multiplied (these are the factors). These two numbers will then each have their own branches. This is done until the original number is broken down into its prime factors.

Worked examples

\(36\) splits into \(6 \times 6\); each \(6\) splits into \(2 \times 3\); final: \(2^2 \times 3^2\)

Branch until every leaf is prime; the primes at the bottom are the prime factorization.

\(45\) splits into \(5 \times 9\); \(9\) splits into \(3 \times 3\); final: \(3^2 \times 5\)

You can start with any factor pair; the tree always gives the same set of prime factors.

Common mistakes

\(36 = 4 \times 9\); stop here because \(4\) and \(9\) are factors → \(36 = 4 \times 9 = (2 \times 2) \times (3 \times 3) = 2^2 \times 3^2\) You must continue branching until every factor is prime; 4 and 9 are composite.
\(30 = 2 \times 15\); write \(2 \times 15\) as the prime factorization → \(30 = 2 \times 15 = 2 \times 3 \times 5\) 15 is not prime — branch it into 3 and 5.
Include \(1\) as a factor at the bottom of the tree → Only write prime numbers (2, 3, 5, 7, …) at the leaves 1 is not prime and does not appear in prime factorizations.

Where you'll use it next

Factor trees prepare you for finding GCF and LCM, simplifying radicals and fractions, solving Diophantine equations, and understanding divisibility in number theory and algebra.

Found in 1 StudyPug lesson

Prime Factorization: Mastering Division by Primes

8th Grade Math

Unlock the power of prime factorization with our step-by-step guide. Learn essential techniques, from factor trees to the ladder method, and boost your math prowess. Perfect for students of all levels!

8th Grade8th