The GCD of given numbers is 9.
Step 1 :
Divide $ 72 $ by $ 63 $ and get the remainder
The remainder is positive ($ 9 > 0 $), so we will continue with division.
Step 2 :
Divide $ 63 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 9 }} $.
We can summarize an algorithm into a following table.
72 | : | 63 | = | 1 | remainder ( 9 ) | ||
63 | : | 9 | = | 7 | remainder ( 0 ) | ||
GCD = 9 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.