The GCD of given numbers is 15.
Step 1 :
Divide $ 1875 $ by $ 135 $ and get the remainder
The remainder is positive ($ 120 > 0 $), so we will continue with division.
Step 2 :
Divide $ 135 $ by $ \color{blue}{ 120 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 3 :
Divide $ 120 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 15 }} $.
We can summarize an algorithm into a following table.
1875 | : | 135 | = | 13 | remainder ( 120 ) | ||||
135 | : | 120 | = | 1 | remainder ( 15 ) | ||||
120 | : | 15 | = | 8 | remainder ( 0 ) | ||||
GCD = 15 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.