The GCD of given numbers is 11.
Step 1 :
Divide $ 100001 $ by $ 1001 $ and get the remainder
The remainder is positive ($ 902 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1001 $ by $ \color{blue}{ 902 } $ and get the remainder
The remainder is still positive ($ 99 > 0 $), so we will continue with division.
Step 3 :
Divide $ 902 $ by $ \color{blue}{ 99 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 4 :
Divide $ 99 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.
We can summarize an algorithm into a following table.
100001 | : | 1001 | = | 99 | remainder ( 902 ) | ||||||
1001 | : | 902 | = | 1 | remainder ( 99 ) | ||||||
902 | : | 99 | = | 9 | remainder ( 11 ) | ||||||
99 | : | 11 | = | 9 | remainder ( 0 ) | ||||||
GCD = 11 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.