The GCD of given numbers is 34.
Step 1 :
Divide $ 442 $ by $ 272 $ and get the remainder
The remainder is positive ($ 170 > 0 $), so we will continue with division.
Step 2 :
Divide $ 272 $ by $ \color{blue}{ 170 } $ and get the remainder
The remainder is still positive ($ 102 > 0 $), so we will continue with division.
Step 3 :
Divide $ 170 $ by $ \color{blue}{ 102 } $ and get the remainder
The remainder is still positive ($ 68 > 0 $), so we will continue with division.
Step 4 :
Divide $ 102 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 34 > 0 $), so we will continue with division.
Step 5 :
Divide $ 68 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 34 }} $.
We can summarize an algorithm into a following table.
442 | : | 272 | = | 1 | remainder ( 170 ) | ||||||||
272 | : | 170 | = | 1 | remainder ( 102 ) | ||||||||
170 | : | 102 | = | 1 | remainder ( 68 ) | ||||||||
102 | : | 68 | = | 1 | remainder ( 34 ) | ||||||||
68 | : | 34 | = | 2 | remainder ( 0 ) | ||||||||
GCD = 34 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.