Find Greatest Common Divisor of 84 and 320, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 320 $ by $ 84 $ and get the remainder
The remainder is positive ($ 68 > 0 $), so we will continue with division.
Step 2 :
Divide $ 84 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 3 :
Divide $ 68 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 4 :
Divide $ 16 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 320 | : | 84 | = | 3 | remainder ( 68 ) | ||||||
| 84 | : | 68 | = | 1 | remainder ( 16 ) | ||||||
| 68 | : | 16 | = | 4 | remainder ( 4 ) | ||||||
| 16 | : | 4 | = | 4 | remainder ( 0 ) | ||||||
| GCD = 4 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.