Math proof regarding gcd

Here is a problem :
Prove if gcd (a,b) = e then gcd (a, b/e)= 1

Hint : use the fact that gcd(a,bc)= gcd(a,b) gcd(a,c)

Please help me I am lost

Quote:

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Originally Posted by tareksha

Here is a problem :
Prove if gcd (a,b) = e then gcd (a, b/e)= 1

Hint : use the fact that gcd(a,bc)= gcd(a,b) gcd(a,c)

Please help me I am lost

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I have a counterexample: gcd (6, 4) = 2 but gcd (6, 4/2) = gcd (6, 2) = 2

A counterexample for the hint would be: gcd (6, 4) = 2 whereas gcd (6, 2)*gcd (6, 2) = 4

Quote:

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Originally Posted by alexmahone

I have a counterexample: gcd (6, 4) = 2 but gcd (6, 4/2) = gcd (6, 2) = 2

A counterexample for the hint would be: gcd (6, 4) = 2 whereas gcd (6, 2)*gcd (6, 2) = 4

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Thank you so much brother . I appreciate your response