GCD with a prime

#gcd#prime#divisor

Statement

Compute $\gcd(15,7)$ and $\gcd(15,5)$ , using the fact that $7$ and $5$ are prime.

Hint

$\gcd(n,p)$ is either $1$ or $p$ when $p$ is prime.

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$\gcd(15,7)$ . $7\nmid15$ , so $\gcd=1$ .

$\gcd(15,5)$ . $5\mid15$ , so $\gcd=5$ .

Conclusion. $\gcd(15,7)=1$ , $\gcd(15,5)=5$ .