Generate an equivalent expression using prime factorization for 432.

BRAINLEST PLEASE?

]What is the prime factorization of the number 432?

A:

The prime factors are: 2 x 2 x 2 x 2 x 3 x 3 x 3

or also written as { 2, 2, 2, 2, 3, 3, 3 }

Written in exponential form: 24 x 33

Step-by-step explanation:

Why is the prime factorization of 432 written as 24 x 33?

What is prime factorization?

Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.

Finding the prime factors of 432

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 432 by 2

432 ÷ 2 = 216 - No remainder! 2 is one of the factors!

216 ÷ 2 = 108 - No remainder! 2 is one of the factors!

108 ÷ 2 = 54 - No remainder! 2 is one of the factors!

54 ÷ 2 = 27 - No remainder! 2 is one of the factors!

27 ÷ 2 = 13.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number

27 ÷ 3 = 9 - No remainder! 3 is one of the factors!

9 ÷ 3 = 3 - No remainder! 3 is one of the factors!

3 ÷ 3 = 1 - No remainder! 3 is one of the factors!

The orange divisor(s) above are the prime factors of the number 432. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 3 x 3 = 432. It can also be written in exponential form as 24 x 33.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 432.

432      

Factor Arrows      

2  216    

Factor Arrows    

2  108    

Factor Arrows    

2  54  

Factor Arrows  

2  27  

Factor Arrows  

3  9

Factor Arrows

3  3

14

step-by-step explanation:

14 x 3 = 42