Work Step by Step
The first step is to write 54 at the top of your factor tree. The next question is what 2 numbers multiply together to get 54. For this example, I used 6 and 9. So, 6 and 9 are written under the 54 as 2 different "branches." For each new number "branching" out from the previous number, you must determine if it is prime. 6 is not prime because 3 and 2 are another set of factors for 6 besides 6 itself. Now, both 3 and 2 are prime, so circle the numbers 3 and 2 separately to show their separation from the rest of the factor tree. 9 is also not prime because 3 and 3 are another set of factors for 9 besides 9 itself. Now, 3 and 3 are both prime, so circle each number separately. Looking at all 4 circled numbers, $2\times3\times3\times3$ would be the prime factorization for 27.