The GCD of given numbers is 14.
Step 1 :
Divide $ 2282 $ by $ 420 $ and get the remainder
The remainder is positive ($ 182 > 0 $), so we will continue with division.
Step 2 :
Divide $ 420 $ by $ \color{blue}{ 182 } $ and get the remainder
The remainder is still positive ($ 56 > 0 $), so we will continue with division.
Step 3 :
Divide $ 182 $ by $ \color{blue}{ 56 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 4 :
Divide $ 56 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 14 }} $.
We can summarize an algorithm into a following table.
2282 | : | 420 | = | 5 | remainder ( 182 ) | ||||||
420 | : | 182 | = | 2 | remainder ( 56 ) | ||||||
182 | : | 56 | = | 3 | remainder ( 14 ) | ||||||
56 | : | 14 | = | 4 | remainder ( 0 ) | ||||||
GCD = 14 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.