Find Greatest Common Divisor of 5504 and 385, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 5504 $ by $ 385 $ and get the remainder
The remainder is positive ($ 114 > 0 $), so we will continue with division.
Step 2 :
Divide $ 385 $ by $ \color{blue}{ 114 } $ and get the remainder
The remainder is still positive ($ 43 > 0 $), so we will continue with division.
Step 3 :
Divide $ 114 $ by $ \color{blue}{ 43 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 4 :
Divide $ 43 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 5 :
Divide $ 28 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 6 :
Divide $ 15 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 13 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
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.
| 5504 | : | 385 | = | 14 | remainder ( 114 ) | ||||||||||||||
| 385 | : | 114 | = | 3 | remainder ( 43 ) | ||||||||||||||
| 114 | : | 43 | = | 2 | remainder ( 28 ) | ||||||||||||||
| 43 | : | 28 | = | 1 | remainder ( 15 ) | ||||||||||||||
| 28 | : | 15 | = | 1 | remainder ( 13 ) | ||||||||||||||
| 15 | : | 13 | = | 1 | remainder ( 2 ) | ||||||||||||||
| 13 | : | 2 | = | 6 | 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.