Find Greatest Common Divisor of 16261 and 85652, using Euclidean algorithm.
Answer
The GCD of given numbers is 161.
Explanation
Step 1 :
Divide $ 85652 $ by $ 16261 $ and get the remainder
The remainder is positive ($ 4347 > 0 $), so we will continue with division.
Step 2 :
Divide $ 16261 $ by $ \color{blue}{ 4347 } $ and get the remainder
The remainder is still positive ($ 3220 > 0 $), so we will continue with division.
Step 3 :
Divide $ 4347 $ by $ \color{blue}{ 3220 } $ and get the remainder
The remainder is still positive ($ 1127 > 0 $), so we will continue with division.
Step 4 :
Divide $ 3220 $ by $ \color{blue}{ 1127 } $ and get the remainder
The remainder is still positive ($ 966 > 0 $), so we will continue with division.
Step 5 :
Divide $ 1127 $ by $ \color{blue}{ 966 } $ and get the remainder
The remainder is still positive ($ 161 > 0 $), so we will continue with division.
Step 6 :
Divide $ 966 $ by $ \color{blue}{ 161 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 161 }} $.
We can summarize an algorithm into a following table.
| 85652 | : | 16261 | = | 5 | remainder ( 4347 ) | ||||||||||
| 16261 | : | 4347 | = | 3 | remainder ( 3220 ) | ||||||||||
| 4347 | : | 3220 | = | 1 | remainder ( 1127 ) | ||||||||||
| 3220 | : | 1127 | = | 2 | remainder ( 966 ) | ||||||||||
| 1127 | : | 966 | = | 1 | remainder ( 161 ) | ||||||||||
| 966 | : | 161 | = | 6 | remainder ( 0 ) | ||||||||||
| GCD = 161 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.