The GCD of given numbers is 15.
Step 1 :
Divide $ 1320 $ by $ 1065 $ and get the remainder
The remainder is positive ($ 255 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1065 $ by $ \color{blue}{ 255 } $ and get the remainder
The remainder is still positive ($ 45 > 0 $), so we will continue with division.
Step 3 :
Divide $ 255 $ by $ \color{blue}{ 45 } $ and get the remainder
The remainder is still positive ($ 30 > 0 $), so we will continue with division.
Step 4 :
Divide $ 45 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 5 :
Divide $ 30 $ 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.
1320 | : | 1065 | = | 1 | remainder ( 255 ) | ||||||||
1065 | : | 255 | = | 4 | remainder ( 45 ) | ||||||||
255 | : | 45 | = | 5 | remainder ( 30 ) | ||||||||
45 | : | 30 | = | 1 | remainder ( 15 ) | ||||||||
30 | : | 15 | = | 2 | remainder ( 0 ) | ||||||||
GCD = 15 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.