Using the greatest common factor, simplify the fraction 160200

Question

(1 point)
Responses

45
4 fifths

1620
16 over 20

4050
40 over 50

40

Answer 1

To simplify the fraction 160200, we need to find the greatest common factor (GCF) of the numerator and denominator.

However, the fraction appears to be missing a denominator. Assuming it is meant to be written as $\frac{160}{200}$, let's simplify this.

1. The prime factors of 160 are $2^5\times 5$.
2. The prime factors of 200 are $2^3\times 5^2$.

To find the GCF, we take the lowest powers of the common factors:

• For $2$, the minimum power is $2^3$.
• For $5$, the minimum power is $5^1$.

Thus, the GCF is $2^3\times 5^1=8\times 5=40$.

Now, we can simplify $\frac{160}{200}$ using the GCF:

$$\frac{160÷40}{200÷40}=\frac{4}{5}$$

Therefore, the simplified fraction is $\frac{4}{5}$.

The correct simplification based on the options provided is:

4 fifths.