The GCD of given numbers is 4.
Step 1 :
Divide $ 356 $ by $ 252 $ and get the remainder
The remainder is positive ($ 104 > 0 $), so we will continue with division.
Step 2 :
Divide $ 252 $ by $ \color{blue}{ 104 } $ and get the remainder
The remainder is still positive ($ 44 > 0 $), so we will continue with division.
Step 3 :
Divide $ 104 $ by $ \color{blue}{ 44 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 4 :
Divide $ 44 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 5 :
Divide $ 16 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 12 $ 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.
356 | : | 252 | = | 1 | remainder ( 104 ) | ||||||||||
252 | : | 104 | = | 2 | remainder ( 44 ) | ||||||||||
104 | : | 44 | = | 2 | remainder ( 16 ) | ||||||||||
44 | : | 16 | = | 2 | remainder ( 12 ) | ||||||||||
16 | : | 12 | = | 1 | remainder ( 4 ) | ||||||||||
12 | : | 4 | = | 3 | remainder ( 0 ) | ||||||||||
GCD = 4 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.