The GCD of given numbers is 1.
Step 1 :
Divide $ 722 $ by $ 461 $ and get the remainder
The remainder is positive ($ 261 > 0 $), so we will continue with division.
Step 2 :
Divide $ 461 $ by $ \color{blue}{ 261 } $ and get the remainder
The remainder is still positive ($ 200 > 0 $), so we will continue with division.
Step 3 :
Divide $ 261 $ by $ \color{blue}{ 200 } $ and get the remainder
The remainder is still positive ($ 61 > 0 $), so we will continue with division.
Step 4 :
Divide $ 200 $ by $ \color{blue}{ 61 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 5 :
Divide $ 61 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 6 :
Divide $ 17 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 7 :
Divide $ 10 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 8 :
Divide $ 7 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 9 :
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.
722 | : | 461 | = | 1 | remainder ( 261 ) | ||||||||||||||||
461 | : | 261 | = | 1 | remainder ( 200 ) | ||||||||||||||||
261 | : | 200 | = | 1 | remainder ( 61 ) | ||||||||||||||||
200 | : | 61 | = | 3 | remainder ( 17 ) | ||||||||||||||||
61 | : | 17 | = | 3 | remainder ( 10 ) | ||||||||||||||||
17 | : | 10 | = | 1 | remainder ( 7 ) | ||||||||||||||||
10 | : | 7 | = | 1 | remainder ( 3 ) | ||||||||||||||||
7 | : | 3 | = | 2 | 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.