The GCD of given numbers is 2.
Step 1 :
Divide $ 1874 $ by $ 602 $ and get the remainder
The remainder is positive ($ 68 > 0 $), so we will continue with division.
Step 2 :
Divide $ 602 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 58 > 0 $), so we will continue with division.
Step 3 :
Divide $ 68 $ by $ \color{blue}{ 58 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 4 :
Divide $ 58 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 10 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 6 :
Divide $ 8 $ 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.
1874 | : | 602 | = | 3 | remainder ( 68 ) | ||||||||||
602 | : | 68 | = | 8 | remainder ( 58 ) | ||||||||||
68 | : | 58 | = | 1 | remainder ( 10 ) | ||||||||||
58 | : | 10 | = | 5 | remainder ( 8 ) | ||||||||||
10 | : | 8 | = | 1 | remainder ( 2 ) | ||||||||||
8 | : | 2 | = | 4 | remainder ( 0 ) | ||||||||||
GCD = 2 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.