The GCD of given numbers is 7.
Step 1 :
Divide $ 1547 $ by $ 560 $ and get the remainder
The remainder is positive ($ 427 > 0 $), so we will continue with division.
Step 2 :
Divide $ 560 $ by $ \color{blue}{ 427 } $ and get the remainder
The remainder is still positive ($ 133 > 0 $), so we will continue with division.
Step 3 :
Divide $ 427 $ by $ \color{blue}{ 133 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 4 :
Divide $ 133 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 5 :
Divide $ 28 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 6 :
Divide $ 21 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
1547 | : | 560 | = | 2 | remainder ( 427 ) | ||||||||||
560 | : | 427 | = | 1 | remainder ( 133 ) | ||||||||||
427 | : | 133 | = | 3 | remainder ( 28 ) | ||||||||||
133 | : | 28 | = | 4 | remainder ( 21 ) | ||||||||||
28 | : | 21 | = | 1 | remainder ( 7 ) | ||||||||||
21 | : | 7 | = | 3 | remainder ( 0 ) | ||||||||||
GCD = 7 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.