The GCD of given numbers is 1.
Step 1 :
Divide $ 504 $ by $ 295 $ and get the remainder
The remainder is positive ($ 209 > 0 $), so we will continue with division.
Step 2 :
Divide $ 295 $ by $ \color{blue}{ 209 } $ and get the remainder
The remainder is still positive ($ 86 > 0 $), so we will continue with division.
Step 3 :
Divide $ 209 $ by $ \color{blue}{ 86 } $ and get the remainder
The remainder is still positive ($ 37 > 0 $), so we will continue with division.
Step 4 :
Divide $ 86 $ by $ \color{blue}{ 37 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 5 :
Divide $ 37 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 12 $ 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.
504 | : | 295 | = | 1 | remainder ( 209 ) | ||||||||||
295 | : | 209 | = | 1 | remainder ( 86 ) | ||||||||||
209 | : | 86 | = | 2 | remainder ( 37 ) | ||||||||||
86 | : | 37 | = | 2 | remainder ( 12 ) | ||||||||||
37 | : | 12 | = | 3 | remainder ( 1 ) | ||||||||||
12 | : | 1 | = | 12 | remainder ( 0 ) | ||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.