Find Greatest Common Divisor of 1002 and 558, using Euclidean algorithm.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 :
Divide $ 1002 $ by $ 558 $ and get the remainder
The remainder is positive ($ 444 > 0 $), so we will continue with division.
Step 2 :
Divide $ 558 $ by $ \color{blue}{ 444 } $ and get the remainder
The remainder is still positive ($ 114 > 0 $), so we will continue with division.
Step 3 :
Divide $ 444 $ by $ \color{blue}{ 114 } $ and get the remainder
The remainder is still positive ($ 102 > 0 $), so we will continue with division.
Step 4 :
Divide $ 114 $ by $ \color{blue}{ 102 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 5 :
Divide $ 102 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 6 :
Divide $ 12 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.
We can summarize an algorithm into a following table.
| 1002 | : | 558 | = | 1 | remainder ( 444 ) | ||||||||||
| 558 | : | 444 | = | 1 | remainder ( 114 ) | ||||||||||
| 444 | : | 114 | = | 3 | remainder ( 102 ) | ||||||||||
| 114 | : | 102 | = | 1 | remainder ( 12 ) | ||||||||||
| 102 | : | 12 | = | 8 | remainder ( 6 ) | ||||||||||
| 12 | : | 6 | = | 2 | remainder ( 0 ) | ||||||||||
| GCD = 6 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.