The GCD of given numbers is 38.
Step 1 :
Divide $ 3762 $ by $ 1634 $ and get the remainder
The remainder is positive ($ 494 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1634 $ by $ \color{blue}{ 494 } $ and get the remainder
The remainder is still positive ($ 152 > 0 $), so we will continue with division.
Step 3 :
Divide $ 494 $ by $ \color{blue}{ 152 } $ and get the remainder
The remainder is still positive ($ 38 > 0 $), so we will continue with division.
Step 4 :
Divide $ 152 $ by $ \color{blue}{ 38 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 38 }} $.
We can summarize an algorithm into a following table.
3762 | : | 1634 | = | 2 | remainder ( 494 ) | ||||||
1634 | : | 494 | = | 3 | remainder ( 152 ) | ||||||
494 | : | 152 | = | 3 | remainder ( 38 ) | ||||||
152 | : | 38 | = | 4 | remainder ( 0 ) | ||||||
GCD = 38 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.