The GCD of given numbers is 18.
Step 1 :
Divide $ 1170 $ by $ 972 $ and get the remainder
The remainder is positive ($ 198 > 0 $), so we will continue with division.
Step 2 :
Divide $ 972 $ by $ \color{blue}{ 198 } $ and get the remainder
The remainder is still positive ($ 180 > 0 $), so we will continue with division.
Step 3 :
Divide $ 198 $ by $ \color{blue}{ 180 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 4 :
Divide $ 180 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 18 }} $.
We can summarize an algorithm into a following table.
1170 | : | 972 | = | 1 | remainder ( 198 ) | ||||||
972 | : | 198 | = | 4 | remainder ( 180 ) | ||||||
198 | : | 180 | = | 1 | remainder ( 18 ) | ||||||
180 | : | 18 | = | 10 | remainder ( 0 ) | ||||||
GCD = 18 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.