The GCD of given numbers is 1.
Step 1 :
Divide $ 1045 $ by $ 97 $ and get the remainder
The remainder is positive ($ 75 > 0 $), so we will continue with division.
Step 2 :
Divide $ 97 $ by $ \color{blue}{ 75 } $ and get the remainder
The remainder is still positive ($ 22 > 0 $), so we will continue with division.
Step 3 :
Divide $ 75 $ by $ \color{blue}{ 22 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 4 :
Divide $ 22 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
Divide $ 9 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 4 $ 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.
1045 | : | 97 | = | 10 | remainder ( 75 ) | ||||||||||
97 | : | 75 | = | 1 | remainder ( 22 ) | ||||||||||
75 | : | 22 | = | 3 | remainder ( 9 ) | ||||||||||
22 | : | 9 | = | 2 | remainder ( 4 ) | ||||||||||
9 | : | 4 | = | 2 | remainder ( 1 ) | ||||||||||
4 | : | 1 | = | 4 | remainder ( 0 ) | ||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.