Find Greatest Common Divisor of 527 and 765, using Euclidean algorithm.
Answer
The GCD of given numbers is 17.
Explanation
Step 1 :
Divide $ 765 $ by $ 527 $ and get the remainder
The remainder is positive ($ 238 > 0 $), so we will continue with division.
Step 2 :
Divide $ 527 $ by $ \color{blue}{ 238 } $ and get the remainder
The remainder is still positive ($ 51 > 0 $), so we will continue with division.
Step 3 :
Divide $ 238 $ by $ \color{blue}{ 51 } $ and get the remainder
The remainder is still positive ($ 34 > 0 $), so we will continue with division.
Step 4 :
Divide $ 51 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 5 :
Divide $ 34 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 17 }} $.
We can summarize an algorithm into a following table.
| 765 | : | 527 | = | 1 | remainder ( 238 ) | ||||||||
| 527 | : | 238 | = | 2 | remainder ( 51 ) | ||||||||
| 238 | : | 51 | = | 4 | remainder ( 34 ) | ||||||||
| 51 | : | 34 | = | 1 | remainder ( 17 ) | ||||||||
| 34 | : | 17 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 17 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.