The GCD of given numbers is 35.
Step 1 :
Divide $ 12075 $ by $ 4655 $ and get the remainder
The remainder is positive ($ 2765 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4655 $ by $ \color{blue}{ 2765 } $ and get the remainder
The remainder is still positive ($ 1890 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2765 $ by $ \color{blue}{ 1890 } $ and get the remainder
The remainder is still positive ($ 875 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1890 $ by $ \color{blue}{ 875 } $ and get the remainder
The remainder is still positive ($ 140 > 0 $), so we will continue with division.
Step 5 :
Divide $ 875 $ by $ \color{blue}{ 140 } $ and get the remainder
The remainder is still positive ($ 35 > 0 $), so we will continue with division.
Step 6 :
Divide $ 140 $ by $ \color{blue}{ 35 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 35 }} $.
We can summarize an algorithm into a following table.
12075 | : | 4655 | = | 2 | remainder ( 2765 ) | ||||||||||
4655 | : | 2765 | = | 1 | remainder ( 1890 ) | ||||||||||
2765 | : | 1890 | = | 1 | remainder ( 875 ) | ||||||||||
1890 | : | 875 | = | 2 | remainder ( 140 ) | ||||||||||
875 | : | 140 | = | 6 | remainder ( 35 ) | ||||||||||
140 | : | 35 | = | 4 | remainder ( 0 ) | ||||||||||
GCD = 35 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.