Find Greatest Common Divisor of 1220 and 228, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 1220 $ by $ 228 $ and get the remainder
The remainder is positive ($ 80 > 0 $), so we will continue with division.
Step 2 :
Divide $ 228 $ by $ \color{blue}{ 80 } $ and get the remainder
The remainder is still positive ($ 68 > 0 $), so we will continue with division.
Step 3 :
Divide $ 80 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 4 :
Divide $ 68 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 12 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 8 $ 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.
| 1220 | : | 228 | = | 5 | remainder ( 80 ) | ||||||||||
| 228 | : | 80 | = | 2 | remainder ( 68 ) | ||||||||||
| 80 | : | 68 | = | 1 | remainder ( 12 ) | ||||||||||
| 68 | : | 12 | = | 5 | remainder ( 8 ) | ||||||||||
| 12 | : | 8 | = | 1 | remainder ( 4 ) | ||||||||||
| 8 | : | 4 | = | 2 | remainder ( 0 ) | ||||||||||
| GCD = 4 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.