Using the greatest common factor, simplify the fraction 160/200

Question

(1 point)
Responses

4/5
4 fifths

16/20
16 over 20

40/50
40 over 50

40
40

Answer 1

To simplify the fraction \( \frac{160}{200} \) using the greatest common factor (GCF), we first find the GCF of 160 and 200.

The factors of each number are:

• Factors of 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
• Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

The GCF of 160 and 200 is 40.

Now, we can simplify the fraction by dividing both the numerator and denominator by their GCF:

\[ \frac{160 \div 40}{200 \div 40} = \frac{4}{5} \]

Therefore, the simplified fraction is \( \frac{4}{5} \) or 4 fifths.

The correct responses are:

• \( \frac{4}{5} \)
• 4 fifths