Gcd of two number divides each other
114667
$d\mid a,b \iff d\mid\gcd(a,b) \ $ [GCD Universal Property]
73972
How to prove that $\gcd(2n^3-14n+2,n+3) = \gcd(n+3,10)$?
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
53777
Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
127993
Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
93930
GCD of the already GCD
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
1197
Finding $\gcd(2n-1,2n+1)$ . . . I think it's 1 but is my logic right?
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
118809
If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
41295
Divisibility, LCM and GCD for fractions (rationals)