find prime factorization of 108 by using the factor tree method in your notebook.
The Correct Answer and Explanation is:
Prime Factorization of 108 Using the Factor Tree Method
Answer:
108
↙️ ↘️
2 54
↙️ ↘️
2 27
↙️ ↘️
3 9
↙️ ↘️
3 3
So, the prime factorization of 108 is:
108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³
Explanation:
Prime factorization is the process of breaking a number down into a product of prime numbers. Prime numbers are numbers greater than 1 that have only two factors — one and themselves. Some examples include 2, 3, 5, 7, 11, and so on.
To find the prime factorization of 108 using the factor tree method, we begin by dividing the number into any two factors. One of the easiest ways is to start with the smallest prime number that divides it. Since 108 is an even number, we can divide it by 2.
108 ÷ 2 = 54
So, we write 108 as 2 × 54.
Next, we continue factoring 54. Since it is also even, we divide it by 2 again.
54 ÷ 2 = 27
Now we have: 2 × 2 × 27
Next, we factor 27. It is not divisible by 2, but it is divisible by 3.
27 ÷ 3 = 9
So far we have: 2 × 2 × 3 × 9
Now factor 9, which is also divisible by 3.
9 ÷ 3 = 3
So, 9 = 3 × 3
Putting all factors together:
2 × 2 × 3 × 3 × 3
Now, we can write this in exponential form to make it more compact:
2² × 3³
This method helps ensure we include all prime numbers in the factorization. Using a factor tree is a visual and logical way to find the prime building blocks of a number. It is especially useful for breaking down large numbers into simpler components.
