The GCD of given numbers is 17.
Step 1 :
Divide $ 1258 $ by $ 527 $ and get the remainder
The remainder is positive ($ 204 > 0 $), so we will continue with division.
Step 2 :
Divide $ 527 $ by $ \color{blue}{ 204 } $ and get the remainder
The remainder is still positive ($ 119 > 0 $), so we will continue with division.
Step 3 :
Divide $ 204 $ by $ \color{blue}{ 119 } $ and get the remainder
The remainder is still positive ($ 85 > 0 $), so we will continue with division.
Step 4 :
Divide $ 119 $ by $ \color{blue}{ 85 } $ and get the remainder
The remainder is still positive ($ 34 > 0 $), so we will continue with division.
Step 5 :
Divide $ 85 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 6 :
Divide $ 34 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 17 }} $.
We can summarize an algorithm into a following table.
1258 | : | 527 | = | 2 | remainder ( 204 ) | ||||||||||
527 | : | 204 | = | 2 | remainder ( 119 ) | ||||||||||
204 | : | 119 | = | 1 | remainder ( 85 ) | ||||||||||
119 | : | 85 | = | 1 | remainder ( 34 ) | ||||||||||
85 | : | 34 | = | 2 | remainder ( 17 ) | ||||||||||
34 | : | 17 | = | 2 | remainder ( 0 ) | ||||||||||
GCD = 17 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.