Find Greatest Common Divisor of 700 and 179, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 700 $ by $ 179 $ and get the remainder
The remainder is positive ($ 163 > 0 $), so we will continue with division.
Step 2 :
Divide $ 179 $ by $ \color{blue}{ 163 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 3 :
Divide $ 163 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 4 :
Divide $ 16 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 3 $ 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.
| 700 | : | 179 | = | 3 | remainder ( 163 ) | ||||||||
| 179 | : | 163 | = | 1 | remainder ( 16 ) | ||||||||
| 163 | : | 16 | = | 10 | remainder ( 3 ) | ||||||||
| 16 | : | 3 | = | 5 | remainder ( 1 ) | ||||||||
| 3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.