which of these is part of the prime factorization of 80?

Question

2^4
2^2 x 4
2 x 5^2
5^4

Answer 1

To find the prime factorization of 80, we can start by dividing it by the smallest prime numbers.

1. $80÷2=40$
2. $40÷2=20$
3. $20÷2=10$
4. $10÷2=5$

Now, we cannot divide 5 by 2, but it is a prime number.

So we have:

$$80=2\times 2\times 2\times 2\times 5=2^4\times 5^1$$

Now we can analyze the given options:

1. $2^4$ - This is a part of the factorization (it includes the 2's).
2. $2^2\times 4$ - This can be broken down to $2^2\times 2^2=2^4$, so it represents the same quantity and is part of the prime factorization.
3. $2\times 5^2$ - This is not part of the factorization, as we only have $5^1$ in the factorization of 80.
4. $5^4$ - This is also not part of the factorization, as we only have $5^1$.

So, the choices that are part of the prime factorization of 80 are $2^4$ and $2^2\times 4$.