The GCD of given numbers is 5.
Step 1 :
Divide $ 845 $ by $ 745 $ and get the remainder
The remainder is positive ($ 100 > 0 $), so we will continue with division.
Step 2 :
Divide $ 745 $ by $ \color{blue}{ 100 } $ and get the remainder
The remainder is still positive ($ 45 > 0 $), so we will continue with division.
Step 3 :
Divide $ 100 $ by $ \color{blue}{ 45 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 4 :
Divide $ 45 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 5 :
Divide $ 10 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 5 }} $.
We can summarize an algorithm into a following table.
845 | : | 745 | = | 1 | remainder ( 100 ) | ||||||||
745 | : | 100 | = | 7 | remainder ( 45 ) | ||||||||
100 | : | 45 | = | 2 | remainder ( 10 ) | ||||||||
45 | : | 10 | = | 4 | remainder ( 5 ) | ||||||||
10 | : | 5 | = | 2 | remainder ( 0 ) | ||||||||
GCD = 5 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.