Find greatest common divisor using Euclidean Algorithm. Find $gcd(56,72) $ using Euclidean Algorithm.

Example: Find $gcd(56,72) $ using Euclidean Algorithm.

Solution: To find  $gcd(56,72) $ using Euclidean Algorithm. We have to apply Division Algorithm to integers $56$ and $72$. Firstly we divide $72$ by $56$. When we divide $72$ by $56$, we get $q = 1$ (i.e. $1$ is a quotient) and $r = 16$ (i.e. $16$ is a remainder). So we get following system of equations in  Euclidean Algorithm.

$72 = 56~ \cdot ~1 + 16$ 

$56 = 16 ~\cdot~ 3 + 8$

$16 = 8 ~\cdot ~2 + 0$

$8$ is the last nonzero remainder obtained in this Algorithm, so  $gcd(72, 56)  = 8$.




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