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Step-by-step explanation:

GCD Method :

step 1 Address the formula, input parameters & values.

Input parameters & values:

The given fraction = 75/200

step 2 Find GCD (Greatest Common Factor) for both numerator & denominator.

The GCF for 75 & 200 is 25

step 3 divide the numerator & denominator by GCD 25 and rewrite the fraction

= (75/25) / (200/25)

= 3/8

Thus, 3/8 is the simplified fraction for 75/200 by using the GCD or HCF method.

Prime Factorization Method :

step 1 Address input parameters & values.

Input parameters & values:

The given fraction = 75/200

step 2 Find prime factors for both numerator & denominator and rewrite the fraction in the form of prime factors

Prime factors for 75 = 3 x 5 x 5

Prime factors for 200 = 2 x 2 x 2 x 5 x 5

= (3 x 5 x 5) / (2 x 2 x 2 x 5 x 5)

step 3 solve & rewrite the fraction

= (3 )/(2 x 2 x 2 )

= 3/8

Thus, 3/8 is the simplified fraction for 75/200 by using the prime factorization method.