The GCD of given numbers is 29.
Step 1 :
Divide $ 1914 $ by $ 899 $ and get the remainder
The remainder is positive ($ 116 > 0 $), so we will continue with division.
Step 2 :
Divide $ 899 $ by $ \color{blue}{ 116 } $ and get the remainder
The remainder is still positive ($ 87 > 0 $), so we will continue with division.
Step 3 :
Divide $ 116 $ by $ \color{blue}{ 87 } $ and get the remainder
The remainder is still positive ($ 29 > 0 $), so we will continue with division.
Step 4 :
Divide $ 87 $ by $ \color{blue}{ 29 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 29 }} $.
We can summarize an algorithm into a following table.
1914 | : | 899 | = | 2 | remainder ( 116 ) | ||||||
899 | : | 116 | = | 7 | remainder ( 87 ) | ||||||
116 | : | 87 | = | 1 | remainder ( 29 ) | ||||||
87 | : | 29 | = | 3 | remainder ( 0 ) | ||||||
GCD = 29 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.