Using the greatest common factor, simplify the fraction 160/200
A. 4/5
B. 16/20
C. 40/50
D. 40
To simplify the fraction 160/200 using the greatest common factor (GCF), we need to find the largest number that can divide both the numerator (160) and the denominator (200).
The prime factorization of 160 is 2^5 * 5, and the prime factorization of 200 is 2^3 * 5^2.
To find the GCF, we take the smallest exponent for each prime factor that appears in both numbers. In this case, the GCF is 2^3 * 5 = 40.
Now we can divide both the numerator and the denominator by 40:
160/200 = (2^5 * 5)/(2^3 * 5^2)
= (2^3 * 2^2 * 5)/(2^3 * 5^2)
= (2^2 * 5)/(5^2)
= 4/5
Therefore, the simplified fraction is 4/5.
Answer: A. 4/5