Find Greatest Common Divisor of 2437 and 653, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 2437 $ by $ 653 $ and get the remainder
The remainder is positive ($ 478 > 0 $), so we will continue with division.
Step 2 :
Divide $ 653 $ by $ \color{blue}{ 478 } $ and get the remainder
The remainder is still positive ($ 175 > 0 $), so we will continue with division.
Step 3 :
Divide $ 478 $ by $ \color{blue}{ 175 } $ and get the remainder
The remainder is still positive ($ 128 > 0 $), so we will continue with division.
Step 4 :
Divide $ 175 $ by $ \color{blue}{ 128 } $ and get the remainder
The remainder is still positive ($ 47 > 0 $), so we will continue with division.
Step 5 :
Divide $ 128 $ by $ \color{blue}{ 47 } $ and get the remainder
The remainder is still positive ($ 34 > 0 $), so we will continue with division.
Step 6 :
Divide $ 47 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 7 :
Divide $ 34 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 8 :
Divide $ 13 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 9 :
Divide $ 8 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 10 :
Divide $ 5 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 11 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 12 :
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 | : | 653 | = | 3 | remainder ( 478 ) | ||||||||||||||||||||||
| 653 | : | 478 | = | 1 | remainder ( 175 ) | ||||||||||||||||||||||
| 478 | : | 175 | = | 2 | remainder ( 128 ) | ||||||||||||||||||||||
| 175 | : | 128 | = | 1 | remainder ( 47 ) | ||||||||||||||||||||||
| 128 | : | 47 | = | 2 | remainder ( 34 ) | ||||||||||||||||||||||
| 47 | : | 34 | = | 1 | remainder ( 13 ) | ||||||||||||||||||||||
| 34 | : | 13 | = | 2 | remainder ( 8 ) | ||||||||||||||||||||||
| 13 | : | 8 | = | 1 | remainder ( 5 ) | ||||||||||||||||||||||
| 8 | : | 5 | = | 1 | remainder ( 3 ) | ||||||||||||||||||||||
| 5 | : | 3 | = | 1 | remainder ( 2 ) | ||||||||||||||||||||||
| 3 | : | 2 | = | 1 | 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.