The GCD of given numbers is 62.
Step 1 :
Divide $ 682 $ by $ 496 $ and get the remainder
The remainder is positive ($ 186 > 0 $), so we will continue with division.
Step 2 :
Divide $ 496 $ by $ \color{blue}{ 186 } $ and get the remainder
The remainder is still positive ($ 124 > 0 $), so we will continue with division.
Step 3 :
Divide $ 186 $ by $ \color{blue}{ 124 } $ and get the remainder
The remainder is still positive ($ 62 > 0 $), so we will continue with division.
Step 4 :
Divide $ 124 $ by $ \color{blue}{ 62 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 62 }} $.
We can summarize an algorithm into a following table.
682 | : | 496 | = | 1 | remainder ( 186 ) | ||||||
496 | : | 186 | = | 2 | remainder ( 124 ) | ||||||
186 | : | 124 | = | 1 | remainder ( 62 ) | ||||||
124 | : | 62 | = | 2 | remainder ( 0 ) | ||||||
GCD = 62 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.