Prove that of a,b,c are natural numbers

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To prove that if a, b, and c are natural numbers with gcd(a, c) = 1 and b divides c, then gcd(a, b) = 1, one must start by understanding the definition of the greatest common divisor (gcd) and its properties. The gcd of two numbers is the largest positive integer that divides both numbers without leaving a remainder. Given that b divides c, any common divisor of a and b must also divide c, but since gcd(a, c) = 1, a shares no common factors with c. Therefore, the only common divisor between a and b can be 1, leading to the conclusion that gcd(a, b) = 1. This establishes the required proof.
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I would greatly appreciate if someone just at least put me in the right direction with this. I have to prove this:

Prove that of a,b,c are natural numbers, gcd(a,c) = 1 and b divides c, then gcd(a,b) = 1.
 
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Write down the defintion of gcd, what properties does gcd have, in particular gdc(x,y) and dividing x and y. Consider if d is a divisor of b then is it a divisor of c?
 
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