Find Greatest Common Divisor of 285 and 741, using Euclidean algorithm.
Answer
The GCD of given numbers is 57.
Explanation
Step 1 :
Divide $ 741 $ by $ 285 $ and get the remainder
The remainder is positive ($ 171 > 0 $), so we will continue with division.
Step 2 :
Divide $ 285 $ by $ \color{blue}{ 171 } $ and get the remainder
The remainder is still positive ($ 114 > 0 $), so we will continue with division.
Step 3 :
Divide $ 171 $ by $ \color{blue}{ 114 } $ and get the remainder
The remainder is still positive ($ 57 > 0 $), so we will continue with division.
Step 4 :
Divide $ 114 $ by $ \color{blue}{ 57 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 57 }} $.
We can summarize an algorithm into a following table.
| 741 | : | 285 | = | 2 | remainder ( 171 ) | ||||||
| 285 | : | 171 | = | 1 | remainder ( 114 ) | ||||||
| 171 | : | 114 | = | 1 | remainder ( 57 ) | ||||||
| 114 | : | 57 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 57 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.