How to use a factor tree to find the prime factors of 72? A factor tree is a diagram that organizes the factoring process.
- First step is to find two numbers that when multiplied together equal the number we start with.
2 × 36
- Second step is to check the multiplication(of the first step) for numbers that are not primes.
3 × 12
We found 2 prime factors(2, 3) using the factor tree of 72. Now let us explain the process to solving factor trees in more detail. Our goal is to find all prime factors of a given whole number. In each step of our factor tree diagram for 72 we always checked both multiplication numbers if they were primes or not. If one or both of the integers are not prime numbers then this means that we will have to make diagrams for them too. This process continues until only prime numbers are left.
Remember that often a factor tree for the same integer can be solved in more than one correct way! An example of this is the figure 12 where 2*6=12 and 4*3=12. The primes of a factor tree for 12 are the same regardles if we start the factor tree with 2*6 or 4*3.