The GCD of given numbers is 1.
Step 1 :
Divide $ 97 $ by $ 56 $ and get the remainder
The remainder is positive ($ 41 > 0 $), so we will continue with division.
Step 2 :
Divide $ 56 $ by $ \color{blue}{ 41 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 3 :
Divide $ 41 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 4 :
Divide $ 15 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
Divide $ 11 $ 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.
97 | : | 56 | = | 1 | remainder ( 41 ) | ||||||||||||
56 | : | 41 | = | 1 | remainder ( 15 ) | ||||||||||||
41 | : | 15 | = | 2 | remainder ( 11 ) | ||||||||||||
15 | : | 11 | = | 1 | remainder ( 4 ) | ||||||||||||
11 | : | 4 | = | 2 | 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.