Find Greatest Common Divisor of 2437 and 875, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 2437 $ by $ 875 $ and get the remainder
The remainder is positive ($ 687 > 0 $), so we will continue with division.
Step 2 :
Divide $ 875 $ by $ \color{blue}{ 687 } $ and get the remainder
The remainder is still positive ($ 188 > 0 $), so we will continue with division.
Step 3 :
Divide $ 687 $ by $ \color{blue}{ 188 } $ and get the remainder
The remainder is still positive ($ 123 > 0 $), so we will continue with division.
Step 4 :
Divide $ 188 $ by $ \color{blue}{ 123 } $ and get the remainder
The remainder is still positive ($ 65 > 0 $), so we will continue with division.
Step 5 :
Divide $ 123 $ by $ \color{blue}{ 65 } $ and get the remainder
The remainder is still positive ($ 58 > 0 $), so we will continue with division.
Step 6 :
Divide $ 65 $ by $ \color{blue}{ 58 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 7 :
Divide $ 58 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 8 :
Divide $ 7 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 9 :
Divide $ 2 $ 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.
| 2437 | : | 875 | = | 2 | remainder ( 687 ) | ||||||||||||||||
| 875 | : | 687 | = | 1 | remainder ( 188 ) | ||||||||||||||||
| 687 | : | 188 | = | 3 | remainder ( 123 ) | ||||||||||||||||
| 188 | : | 123 | = | 1 | remainder ( 65 ) | ||||||||||||||||
| 123 | : | 65 | = | 1 | remainder ( 58 ) | ||||||||||||||||
| 65 | : | 58 | = | 1 | remainder ( 7 ) | ||||||||||||||||
| 58 | : | 7 | = | 8 | remainder ( 2 ) | ||||||||||||||||
| 7 | : | 2 | = | 3 | remainder ( 1 ) | ||||||||||||||||
| 2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||||||||
| GCD = 1 | |||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.