Find Greatest Common Divisor of 56 and 999, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 999 $ by $ 56 $ and get the remainder
The remainder is positive ($ 47 > 0 $), so we will continue with division.
Step 2 :
Divide $ 56 $ by $ \color{blue}{ 47 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 3 :
Divide $ 47 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 4 :
Divide $ 9 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 2 $ 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.
| 999 | : | 56 | = | 17 | remainder ( 47 ) | ||||||||
| 56 | : | 47 | = | 1 | remainder ( 9 ) | ||||||||
| 47 | : | 9 | = | 5 | remainder ( 2 ) | ||||||||
| 9 | : | 2 | = | 4 | remainder ( 1 ) | ||||||||
| 2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.