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

Question

(1 point)
Responses

45
4 fifths

1620
16 over 20

4050
40 over 50

40

Answer 1

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

1. Find the GCF:

   • The prime factorization of 160 is \( 2^5 \times 5 \).
   • The prime factorization of 200 is \( 2^3 \times 5^2 \).
   • The GCF is found by taking the lowest power of each common prime factor:
     • For \( 2 \): the lowest power is \( 2^3 \).
     • For \( 5 \): the lowest power is \( 5^1 \).
   • Therefore, \( \text{GCF} = 2^3 \times 5^1 = 8 \times 5 = 40 \).

2. Simplify the fraction:

   • Divide both the numerator and the denominator by the GCF: \[ \frac{160 \div 40}{200 \div 40} = \frac{4}{5} \]

So, the simplified fraction is \( \frac{4}{5} \).

Among the responses provided, the correct answer is 4 fifths.