The GCD of given numbers is 1.
Step 1 :
Divide $ 4801 $ by $ 500 $ and get the remainder
The remainder is positive ($ 301 > 0 $), so we will continue with division.
Step 2 :
Divide $ 500 $ by $ \color{blue}{ 301 } $ and get the remainder
The remainder is still positive ($ 199 > 0 $), so we will continue with division.
Step 3 :
Divide $ 301 $ by $ \color{blue}{ 199 } $ and get the remainder
The remainder is still positive ($ 102 > 0 $), so we will continue with division.
Step 4 :
Divide $ 199 $ by $ \color{blue}{ 102 } $ and get the remainder
The remainder is still positive ($ 97 > 0 $), so we will continue with division.
Step 5 :
Divide $ 102 $ by $ \color{blue}{ 97 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 6 :
Divide $ 97 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 5 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
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.
4801 | : | 500 | = | 9 | remainder ( 301 ) | ||||||||||||||
500 | : | 301 | = | 1 | remainder ( 199 ) | ||||||||||||||
301 | : | 199 | = | 1 | remainder ( 102 ) | ||||||||||||||
199 | : | 102 | = | 1 | remainder ( 97 ) | ||||||||||||||
102 | : | 97 | = | 1 | remainder ( 5 ) | ||||||||||||||
97 | : | 5 | = | 19 | 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.