Hello Im having some trouble solving this proof can someone

Hello, I\'m having some trouble solving this proof, can someone please help. Thanks

Let f, g, h and t be integers. If gcd(g, h) = 1 and gcd(g, fh) = t, then gcd(g, f) = t.

Solution

f, g, h and t are integers

GIVEN:

gcd(g, h ) = 1

gcd(g, fh) = t

TO PROVE:

gcd(g, f) = t

PROOF:

For every pair of whole numbers g and h, there exists two integers x and y such that

gx + hy = 1 ----- (Theorem)

Multiplying both sides by f, we get

gf x + hf y = f ----- (1)

t = gcd (g, hf) (given)

from here, t is a common divisor of g and hf

hence, t also divides f by linearity of equation (1)

Every common divisor of two integers also divides their gcd ---------- ( Property )

Since t is a common divisor of both g and f, it also divides their gcd

i.e. gcd (g, f) = t

Hence Proved