Find Greatest Common Divisor of 280 and 117, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 280 $ by $ 117 $ and get the remainder
The remainder is positive ($ 46 > 0 $), so we will continue with division.
Step 2 :
Divide $ 117 $ by $ \color{blue}{ 46 } $ and get the remainder
The remainder is still positive ($ 25 > 0 $), so we will continue with division.
Step 3 :
Divide $ 46 $ by $ \color{blue}{ 25 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 4 :
Divide $ 25 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
Divide $ 21 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 4 $ 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.
| 280 | : | 117 | = | 2 | remainder ( 46 ) | ||||||||||
| 117 | : | 46 | = | 2 | remainder ( 25 ) | ||||||||||
| 46 | : | 25 | = | 1 | remainder ( 21 ) | ||||||||||
| 25 | : | 21 | = | 1 | remainder ( 4 ) | ||||||||||
| 21 | : | 4 | = | 5 | remainder ( 1 ) | ||||||||||
| 4 | : | 1 | = | 4 | remainder ( 0 ) | ||||||||||
| GCD = 1 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.