The GCD of given numbers is 1.
Step 1 :
Divide $ 277 $ by $ 143 $ and get the remainder
The remainder is positive ($ 134 > 0 $), so we will continue with division.
Step 2 :
Divide $ 143 $ by $ \color{blue}{ 134 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 3 :
Divide $ 134 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 4 :
Divide $ 9 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 8 $ 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.
277 | : | 143 | = | 1 | remainder ( 134 ) | ||||||||
143 | : | 134 | = | 1 | remainder ( 9 ) | ||||||||
134 | : | 9 | = | 14 | remainder ( 8 ) | ||||||||
9 | : | 8 | = | 1 | remainder ( 1 ) | ||||||||
8 | : | 1 | = | 8 | remainder ( 0 ) | ||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.