The GCD of given numbers is 9.
Step 1 :
Divide $ 400680 $ by $ 3501 $ and get the remainder
The remainder is positive ($ 1566 > 0 $), so we will continue with division.
Step 2 :
Divide $ 3501 $ by $ \color{blue}{ 1566 } $ and get the remainder
The remainder is still positive ($ 369 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1566 $ by $ \color{blue}{ 369 } $ and get the remainder
The remainder is still positive ($ 90 > 0 $), so we will continue with division.
Step 4 :
Divide $ 369 $ by $ \color{blue}{ 90 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 5 :
Divide $ 90 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 9 }} $.
We can summarize an algorithm into a following table.
400680 | : | 3501 | = | 114 | remainder ( 1566 ) | ||||||||
3501 | : | 1566 | = | 2 | remainder ( 369 ) | ||||||||
1566 | : | 369 | = | 4 | remainder ( 90 ) | ||||||||
369 | : | 90 | = | 4 | remainder ( 9 ) | ||||||||
90 | : | 9 | = | 10 | remainder ( 0 ) | ||||||||
GCD = 9 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.