The GCD of given numbers is 10.
Step 1 :
Divide $ 790 $ by $ 380 $ and get the remainder
The remainder is positive ($ 30 > 0 $), so we will continue with division.
Step 2 :
Divide $ 380 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 3 :
Divide $ 30 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 4 :
Divide $ 20 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.
We can summarize an algorithm into a following table.
790 | : | 380 | = | 2 | remainder ( 30 ) | ||||||
380 | : | 30 | = | 12 | remainder ( 20 ) | ||||||
30 | : | 20 | = | 1 | remainder ( 10 ) | ||||||
20 | : | 10 | = | 2 | remainder ( 0 ) | ||||||
GCD = 10 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.