The GCD of given numbers is 17.
Step 1 :
Divide $ 357 $ by $ 221 $ and get the remainder
The remainder is positive ($ 136 > 0 $), so we will continue with division.
Step 2 :
Divide $ 221 $ by $ \color{blue}{ 136 } $ and get the remainder
The remainder is still positive ($ 85 > 0 $), so we will continue with division.
Step 3 :
Divide $ 136 $ by $ \color{blue}{ 85 } $ and get the remainder
The remainder is still positive ($ 51 > 0 $), so we will continue with division.
Step 4 :
Divide $ 85 $ by $ \color{blue}{ 51 } $ and get the remainder
The remainder is still positive ($ 34 > 0 $), so we will continue with division.
Step 5 :
Divide $ 51 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 6 :
Divide $ 34 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 17 }} $.
We can summarize an algorithm into a following table.
357 | : | 221 | = | 1 | remainder ( 136 ) | ||||||||||
221 | : | 136 | = | 1 | remainder ( 85 ) | ||||||||||
136 | : | 85 | = | 1 | remainder ( 51 ) | ||||||||||
85 | : | 51 | = | 1 | remainder ( 34 ) | ||||||||||
51 | : | 34 | = | 1 | remainder ( 17 ) | ||||||||||
34 | : | 17 | = | 2 | remainder ( 0 ) | ||||||||||
GCD = 17 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.