The GCD of given numbers is 28.
Step 1 :
Divide $ 73556 $ by $ 3444 $ and get the remainder
The remainder is positive ($ 1232 > 0 $), so we will continue with division.
Step 2 :
Divide $ 3444 $ by $ \color{blue}{ 1232 } $ and get the remainder
The remainder is still positive ($ 980 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1232 $ by $ \color{blue}{ 980 } $ and get the remainder
The remainder is still positive ($ 252 > 0 $), so we will continue with division.
Step 4 :
Divide $ 980 $ by $ \color{blue}{ 252 } $ and get the remainder
The remainder is still positive ($ 224 > 0 $), so we will continue with division.
Step 5 :
Divide $ 252 $ by $ \color{blue}{ 224 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 6 :
Divide $ 224 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 28 }} $.
We can summarize an algorithm into a following table.
73556 | : | 3444 | = | 21 | remainder ( 1232 ) | ||||||||||
3444 | : | 1232 | = | 2 | remainder ( 980 ) | ||||||||||
1232 | : | 980 | = | 1 | remainder ( 252 ) | ||||||||||
980 | : | 252 | = | 3 | remainder ( 224 ) | ||||||||||
252 | : | 224 | = | 1 | remainder ( 28 ) | ||||||||||
224 | : | 28 | = | 8 | remainder ( 0 ) | ||||||||||
GCD = 28 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.