Considering the definition of prime number, prime factorization and a property of the potentiation, this factorization is not a prime factorization. The prime factorization is expressed as: 2⁵× 3× 5⁴× 11²
In the first place, a prime number is a natural number greater than 1 that has only two different divisors: itself and 1. That is, a prime number is an integer greater than 1 that is only divided exactly by 1 and itself .
On the other side, the "factors" are the numbers that you multiply together to get another number.
So "factoring into primes" is figuring out what prime numbers you have to multiply together to get the original number.
That is, factoring in prime numbers is writing any number as the multiplication of prime numbers, regardless of the order of the factors.
In this case, you have the factorization: 2²× 3× 5⁴× 8× 11²
This factorization is not a prime factorization. 2,3,5 and 11 are prime numbers, but 8 is not a prime number. This last number can be factored as:
8= 2³
Then, the factorization is expressed as: 2²× 3× 5⁴× 2³× 11²
A property of the potentiation expresses that the product of powers of equal base results in the same base raised to the sum of the exponents of each factor. In this case, 2² and 2³ are two powers with the same base, so the power is expressed as:
2²× 2³= 2²⁺³= 2⁵
Finally, the prime factorization is expressed as: 2⁵× 3× 5⁴× 11²
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