Find Greatest Common Divisor of 91 and 32, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 91 $ by $ 32 $ and get the remainder
The remainder is positive ($ 27 > 0 $), so we will continue with division.
Step 2 :
Divide $ 32 $ by $ \color{blue}{ 27 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 3 :
Divide $ 27 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 4 :
Divide $ 5 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
| 91 | : | 32 | = | 2 | remainder ( 27 ) | ||||||||
| 32 | : | 27 | = | 1 | remainder ( 5 ) | ||||||||
| 27 | : | 5 | = | 5 | remainder ( 2 ) | ||||||||
| 5 | : | 2 | = | 2 | remainder ( 1 ) | ||||||||
| 2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.