Find Greatest Common Divisor of 561 and 84, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 561 $ by $ 84 $ and get the remainder
The remainder is positive ($ 57 > 0 $), so we will continue with division.
Step 2 :
Divide $ 84 $ by $ \color{blue}{ 57 } $ and get the remainder
The remainder is still positive ($ 27 > 0 $), so we will continue with division.
Step 3 :
Divide $ 57 $ by $ \color{blue}{ 27 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 4 :
Divide $ 27 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
| 561 | : | 84 | = | 6 | remainder ( 57 ) | ||||||
| 84 | : | 57 | = | 1 | remainder ( 27 ) | ||||||
| 57 | : | 27 | = | 2 | remainder ( 3 ) | ||||||
| 27 | : | 3 | = | 9 | remainder ( 0 ) | ||||||
| GCD = 3 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.