Find Greatest Common Divisor of 94 and 172, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 172 $ by $ 94 $ and get the remainder
The remainder is positive ($ 78 > 0 $), so we will continue with division.
Step 2 :
Divide $ 94 $ by $ \color{blue}{ 78 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 3 :
Divide $ 78 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 4 :
Divide $ 16 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 5 :
Divide $ 14 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
| 172 | : | 94 | = | 1 | remainder ( 78 ) | ||||||||
| 94 | : | 78 | = | 1 | remainder ( 16 ) | ||||||||
| 78 | : | 16 | = | 4 | remainder ( 14 ) | ||||||||
| 16 | : | 14 | = | 1 | remainder ( 2 ) | ||||||||
| 14 | : | 2 | = | 7 | remainder ( 0 ) | ||||||||
| GCD = 2 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.