Find Greatest Common Divisor of 1056 and 228, using Euclidean algorithm.
Answer
The GCD of given numbers is 12.
Explanation
Step 1 :
Divide $ 1056 $ by $ 228 $ and get the remainder
The remainder is positive ($ 144 > 0 $), so we will continue with division.
Step 2 :
Divide $ 228 $ by $ \color{blue}{ 144 } $ and get the remainder
The remainder is still positive ($ 84 > 0 $), so we will continue with division.
Step 3 :
Divide $ 144 $ by $ \color{blue}{ 84 } $ and get the remainder
The remainder is still positive ($ 60 > 0 $), so we will continue with division.
Step 4 :
Divide $ 84 $ by $ \color{blue}{ 60 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 5 :
Divide $ 60 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 6 :
Divide $ 24 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 12 }} $.
We can summarize an algorithm into a following table.
| 1056 | : | 228 | = | 4 | remainder ( 144 ) | ||||||||||
| 228 | : | 144 | = | 1 | remainder ( 84 ) | ||||||||||
| 144 | : | 84 | = | 1 | remainder ( 60 ) | ||||||||||
| 84 | : | 60 | = | 1 | remainder ( 24 ) | ||||||||||
| 60 | : | 24 | = | 2 | remainder ( 12 ) | ||||||||||
| 24 | : | 12 | = | 2 | remainder ( 0 ) | ||||||||||
| GCD = 12 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.