The GCD of given numbers is 1.
Step 1 :
Divide $ 377 $ by $ 289 $ and get the remainder
The remainder is positive ($ 88 > 0 $), so we will continue with division.
Step 2 :
Divide $ 289 $ by $ \color{blue}{ 88 } $ and get the remainder
The remainder is still positive ($ 25 > 0 $), so we will continue with division.
Step 3 :
Divide $ 88 $ by $ \color{blue}{ 25 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 4 :
Divide $ 25 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 5 :
Divide $ 13 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 12 $ 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.
377 | : | 289 | = | 1 | remainder ( 88 ) | ||||||||||
289 | : | 88 | = | 3 | remainder ( 25 ) | ||||||||||
88 | : | 25 | = | 3 | remainder ( 13 ) | ||||||||||
25 | : | 13 | = | 1 | remainder ( 12 ) | ||||||||||
13 | : | 12 | = | 1 | remainder ( 1 ) | ||||||||||
12 | : | 1 | = | 12 | remainder ( 0 ) | ||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.