The GCD of given numbers is 5.
Step 1 :
Divide $ 7255 $ by $ 2000 $ and get the remainder
The remainder is positive ($ 1255 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2000 $ by $ \color{blue}{ 1255 } $ and get the remainder
The remainder is still positive ($ 745 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1255 $ by $ \color{blue}{ 745 } $ and get the remainder
The remainder is still positive ($ 510 > 0 $), so we will continue with division.
Step 4 :
Divide $ 745 $ by $ \color{blue}{ 510 } $ and get the remainder
The remainder is still positive ($ 235 > 0 $), so we will continue with division.
Step 5 :
Divide $ 510 $ by $ \color{blue}{ 235 } $ and get the remainder
The remainder is still positive ($ 40 > 0 $), so we will continue with division.
Step 6 :
Divide $ 235 $ by $ \color{blue}{ 40 } $ and get the remainder
The remainder is still positive ($ 35 > 0 $), so we will continue with division.
Step 7 :
Divide $ 40 $ by $ \color{blue}{ 35 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 8 :
Divide $ 35 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 5 }} $.
We can summarize an algorithm into a following table.
7255 | : | 2000 | = | 3 | remainder ( 1255 ) | ||||||||||||||
2000 | : | 1255 | = | 1 | remainder ( 745 ) | ||||||||||||||
1255 | : | 745 | = | 1 | remainder ( 510 ) | ||||||||||||||
745 | : | 510 | = | 1 | remainder ( 235 ) | ||||||||||||||
510 | : | 235 | = | 2 | remainder ( 40 ) | ||||||||||||||
235 | : | 40 | = | 5 | remainder ( 35 ) | ||||||||||||||
40 | : | 35 | = | 1 | remainder ( 5 ) | ||||||||||||||
35 | : | 5 | = | 7 | remainder ( 0 ) | ||||||||||||||
GCD = 5 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.