A number is written with the following factorization: 2(to the third power) x 4 x 5. Is this factorization a prime factorization? Explain why or why not.
( No answer choice )
Prime Factorization is finding which prime numbers multiply together to make the original number.
2³ ∙ 4 ∙ 5 isn't a prime factorization because 4 = 2 ∙ 2 = 2²
In this case prime factorization is:
2³ ∙ 4 ∙ 5 = 2³ ∙ 2 ∙ 2 ∙ 5 = 2³ ∙ 2² ∙ 5 = 2³ ⁺ ² ∙ 5 = 2⁵ ∙ 5
I really need help, anyone there?
this does not help me where is ms sue or some
one like her
nvm it does thx
To determine if the factorization 2^3 x 4 x 5 is a prime factorization, we should first understand what a prime factorization is.
A prime factorization is a representation of a number as a product of its prime factors. Prime numbers are numbers that are only divisible by 1 and themselves. In other words, prime factors are the building blocks of a number that cannot be further divided into smaller factors.
Let's break down the given factorization:
2^3 x 4 x 5
2^3 represents 2 cubed, which means multiplying 2 by itself three times: 2 x 2 x 2 = 8. So, 2^3 is equal to 8.
Now, let's simplify the given factorization:
8 x 4 x 5
8 can be further broken down into its prime factors as 2 x 2 x 2. Therefore, we can rewrite the factorization as:
2 x 2 x 2 x 4 x 5
Now, let's simplifies the factorization:
2 x 4 can be further broken down into its prime factors as 2 x 2. So we can rewrite the factorization again as:
2 x 2 x 2 x 2 x 5
Here, we can see that all the factors in the factorization are prime numbers (2 and 5). So the factorization 2^3 x 4 x 5 is already a prime factorization.
To summarize, the given factorization is already in prime factorization form since all the factors are prime numbers and the exponent represents the power to which a prime number is raised.