The GCD of given numbers is 42.
Step 1 :
Divide $ 126 $ by $ 84 $ and get the remainder
The remainder is positive ($ 42 > 0 $), so we will continue with division.
Step 2 :
Divide $ 84 $ by $ \color{blue}{ 42 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 42 }} $.
We can summarize an algorithm into a following table.
126 | : | 84 | = | 1 | remainder ( 42 ) | ||
84 | : | 42 | = | 2 | remainder ( 0 ) | ||
GCD = 42 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.