Find Greatest Common Divisor of 731 and 952, using Euclidean algorithm.
Answer
The GCD of given numbers is 17.
Explanation
Step 1 :
Divide $ 952 $ by $ 731 $ and get the remainder
The remainder is positive ($ 221 > 0 $), so we will continue with division.
Step 2 :
Divide $ 731 $ by $ \color{blue}{ 221 } $ and get the remainder
The remainder is still positive ($ 68 > 0 $), so we will continue with division.
Step 3 :
Divide $ 221 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 4 :
Divide $ 68 $ 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.
| 952 | : | 731 | = | 1 | remainder ( 221 ) | ||||||
| 731 | : | 221 | = | 3 | remainder ( 68 ) | ||||||
| 221 | : | 68 | = | 3 | remainder ( 17 ) | ||||||
| 68 | : | 17 | = | 4 | remainder ( 0 ) | ||||||
| GCD = 17 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.