Is this factorization a prime factorization? 2^2 x 3 x 5^4 x 8 x 11^2
Yes!! 7260000, Is a prime number! :-)
well than what is it wise guy
no, since 8 is not a prime...
Prime numbers are numbers that can only be divided by 1 and itself.
If any of the numbers are divided by ANYTHING besides 1 and itself, it is not a prime number.
Since 8 can be divided by 1, 2, 4, and 8, it is not prime, so this is not a prime factorization.
it is not a prime number..
To determine if the given factorization is a prime factorization, we need to check if each exponent is the lowest power possible while still maintaining the given number.
Let's break down the given factorization:
2^2 x 3 x 5^4 x 8 x 11^2
First, we can simplify the factors that are not prime powers:
8 can be factored into 2 x 2 x 2, so it becomes 2^3.
Now, we can rewrite the whole factorization with these simplifications:
2^2 x 2^3 x 3 x 5^4 x 11^2
Next, we rearrange the factors to have the primes in ascending order:
2^2 x 2^3 x 3 x 5^4 x 11^2 = 2^2 x 2^3 x 3 x 5^4 x 11^2
Since every factor is already in its prime power form, we can confirm that this is indeed a prime factorization.
Note: In a prime factorization, each prime factor must be represented with its lowest possible exponent.