The GCD of given numbers is 1.
Step 1 :
Divide $ 221 $ by $ 45 $ and get the remainder
The remainder is positive ($ 41 > 0 $), so we will continue with division.
Step 2 :
Divide $ 45 $ by $ \color{blue}{ 41 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 3 :
Divide $ 41 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 4 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
221 | : | 45 | = | 4 | remainder ( 41 ) | ||||||
45 | : | 41 | = | 1 | remainder ( 4 ) | ||||||
41 | : | 4 | = | 10 | remainder ( 1 ) | ||||||
4 | : | 1 | = | 4 | remainder ( 0 ) | ||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.