The GCD of given numbers is 1.
Step 1 :
Divide $ 145 $ by $ 82 $ and get the remainder
The remainder is positive ($ 63 > 0 $), so we will continue with division.
Step 2 :
Divide $ 82 $ by $ \color{blue}{ 63 } $ and get the remainder
The remainder is still positive ($ 19 > 0 $), so we will continue with division.
Step 3 :
Divide $ 63 $ by $ \color{blue}{ 19 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 19 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 6 $ 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.
145 | : | 82 | = | 1 | remainder ( 63 ) | ||||||||
82 | : | 63 | = | 1 | remainder ( 19 ) | ||||||||
63 | : | 19 | = | 3 | remainder ( 6 ) | ||||||||
19 | : | 6 | = | 3 | remainder ( 1 ) | ||||||||
6 | : | 1 | = | 6 | remainder ( 0 ) | ||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.