The GCD of given numbers is 2.
Step 1 :
Divide $ 170 $ by $ 122 $ and get the remainder
The remainder is positive ($ 48 > 0 $), so we will continue with division.
Step 2 :
Divide $ 122 $ by $ \color{blue}{ 48 } $ and get the remainder
The remainder is still positive ($ 26 > 0 $), so we will continue with division.
Step 3 :
Divide $ 48 $ by $ \color{blue}{ 26 } $ and get the remainder
The remainder is still positive ($ 22 > 0 $), so we will continue with division.
Step 4 :
Divide $ 26 $ by $ \color{blue}{ 22 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
Divide $ 22 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 6 :
Divide $ 4 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
170 | : | 122 | = | 1 | remainder ( 48 ) | ||||||||||
122 | : | 48 | = | 2 | remainder ( 26 ) | ||||||||||
48 | : | 26 | = | 1 | remainder ( 22 ) | ||||||||||
26 | : | 22 | = | 1 | remainder ( 4 ) | ||||||||||
22 | : | 4 | = | 5 | remainder ( 2 ) | ||||||||||
4 | : | 2 | = | 2 | remainder ( 0 ) | ||||||||||
GCD = 2 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.