The GCD of given numbers is 4.
Step 1 :
Divide $ 544 $ by $ 212 $ and get the remainder
The remainder is positive ($ 120 > 0 $), so we will continue with division.
Step 2 :
Divide $ 212 $ by $ \color{blue}{ 120 } $ and get the remainder
The remainder is still positive ($ 92 > 0 $), so we will continue with division.
Step 3 :
Divide $ 120 $ by $ \color{blue}{ 92 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 4 :
Divide $ 92 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 28 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 8 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
544 | : | 212 | = | 2 | remainder ( 120 ) | ||||||||||
212 | : | 120 | = | 1 | remainder ( 92 ) | ||||||||||
120 | : | 92 | = | 1 | remainder ( 28 ) | ||||||||||
92 | : | 28 | = | 3 | remainder ( 8 ) | ||||||||||
28 | : | 8 | = | 3 | remainder ( 4 ) | ||||||||||
8 | : | 4 | = | 2 | remainder ( 0 ) | ||||||||||
GCD = 4 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.