The GCD of given numbers is 1.
Step 1 :
Divide $ 267 $ by $ 91 $ and get the remainder
The remainder is positive ($ 85 > 0 $), so we will continue with division.
Step 2 :
Divide $ 91 $ by $ \color{blue}{ 85 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 3 :
Divide $ 85 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 6 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
267 | : | 91 | = | 2 | remainder ( 85 ) | ||||||
91 | : | 85 | = | 1 | remainder ( 6 ) | ||||||
85 | : | 6 | = | 14 | remainder ( 1 ) | ||||||
6 | : | 1 | = | 6 | remainder ( 0 ) | ||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.