The GCD of given numbers is 7.
Step 1 :
Divide $ 1267 $ by $ 35 $ and get the remainder
The remainder is positive ($ 7 > 0 $), so we will continue with division.
Step 2 :
Divide $ 35 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
1267 | : | 35 | = | 36 | remainder ( 7 ) | ||
35 | : | 7 | = | 5 | remainder ( 0 ) | ||
GCD = 7 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.