Find Greatest Common Divisor of 816 and 2260, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 2260 $ by $ 816 $ and get the remainder
The remainder is positive ($ 628 > 0 $), so we will continue with division.
Step 2 :
Divide $ 816 $ by $ \color{blue}{ 628 } $ and get the remainder
The remainder is still positive ($ 188 > 0 $), so we will continue with division.
Step 3 :
Divide $ 628 $ by $ \color{blue}{ 188 } $ and get the remainder
The remainder is still positive ($ 64 > 0 $), so we will continue with division.
Step 4 :
Divide $ 188 $ by $ \color{blue}{ 64 } $ and get the remainder
The remainder is still positive ($ 60 > 0 $), so we will continue with division.
Step 5 :
Divide $ 64 $ by $ \color{blue}{ 60 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 60 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 2260 | : | 816 | = | 2 | remainder ( 628 ) | ||||||||||
| 816 | : | 628 | = | 1 | remainder ( 188 ) | ||||||||||
| 628 | : | 188 | = | 3 | remainder ( 64 ) | ||||||||||
| 188 | : | 64 | = | 2 | remainder ( 60 ) | ||||||||||
| 64 | : | 60 | = | 1 | remainder ( 4 ) | ||||||||||
| 60 | : | 4 | = | 15 | remainder ( 0 ) | ||||||||||
| GCD = 4 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.