The GCD of given numbers is 1.
Step 1 :
Divide $ 657 $ by $ 143 $ and get the remainder
The remainder is positive ($ 85 > 0 $), so we will continue with division.
Step 2 :
Divide $ 143 $ by $ \color{blue}{ 85 } $ and get the remainder
The remainder is still positive ($ 58 > 0 $), so we will continue with division.
Step 3 :
Divide $ 85 $ by $ \color{blue}{ 58 } $ and get the remainder
The remainder is still positive ($ 27 > 0 $), so we will continue with division.
Step 4 :
Divide $ 58 $ by $ \color{blue}{ 27 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
Divide $ 27 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 6 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
657 | : | 143 | = | 4 | remainder ( 85 ) | ||||||||||||
143 | : | 85 | = | 1 | remainder ( 58 ) | ||||||||||||
85 | : | 58 | = | 1 | remainder ( 27 ) | ||||||||||||
58 | : | 27 | = | 2 | remainder ( 4 ) | ||||||||||||
27 | : | 4 | = | 6 | remainder ( 3 ) | ||||||||||||
4 | : | 3 | = | 1 | remainder ( 1 ) | ||||||||||||
3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.