Find Greatest Common Divisor of 359 and 125, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 359 $ by $ 125 $ and get the remainder
The remainder is positive ($ 109 > 0 $), so we will continue with division.
Step 2 :
Divide $ 125 $ by $ \color{blue}{ 109 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 3 :
Divide $ 109 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 4 :
Divide $ 16 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 13 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 3 $ 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.
| 359 | : | 125 | = | 2 | remainder ( 109 ) | ||||||||||
| 125 | : | 109 | = | 1 | remainder ( 16 ) | ||||||||||
| 109 | : | 16 | = | 6 | remainder ( 13 ) | ||||||||||
| 16 | : | 13 | = | 1 | remainder ( 3 ) | ||||||||||
| 13 | : | 3 | = | 4 | remainder ( 1 ) | ||||||||||
| 3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||||||
| GCD = 1 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.