The GCD of given numbers is 9.
Step 1 :
Divide $ 54 $ by $ 45 $ and get the remainder
The remainder is positive ($ 9 > 0 $), so we will continue with division.
Step 2 :
Divide $ 45 $ 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.
54 | : | 45 | = | 1 | remainder ( 9 ) | ||
45 | : | 9 | = | 5 | remainder ( 0 ) | ||
GCD = 9 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.