The GCD of given numbers is 1.
Step 1 :
Divide $ 450 $ by $ 397 $ and get the remainder
The remainder is positive ($ 53 > 0 $), so we will continue with division.
Step 2 :
Divide $ 397 $ by $ \color{blue}{ 53 } $ and get the remainder
The remainder is still positive ($ 26 > 0 $), so we will continue with division.
Step 3 :
Divide $ 53 $ by $ \color{blue}{ 26 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 26 $ 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.
450 | : | 397 | = | 1 | remainder ( 53 ) | ||||||
397 | : | 53 | = | 7 | remainder ( 26 ) | ||||||
53 | : | 26 | = | 2 | remainder ( 1 ) | ||||||
26 | : | 1 | = | 26 | remainder ( 0 ) | ||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.