The GCD of given numbers is 6.
Step 1 :
Divide $ 28458 $ by $ 5280 $ and get the remainder
The remainder is positive ($ 2058 > 0 $), so we will continue with division.
Step 2 :
Divide $ 5280 $ by $ \color{blue}{ 2058 } $ and get the remainder
The remainder is still positive ($ 1164 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2058 $ by $ \color{blue}{ 1164 } $ and get the remainder
The remainder is still positive ($ 894 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1164 $ by $ \color{blue}{ 894 } $ and get the remainder
The remainder is still positive ($ 270 > 0 $), so we will continue with division.
Step 5 :
Divide $ 894 $ by $ \color{blue}{ 270 } $ and get the remainder
The remainder is still positive ($ 84 > 0 $), so we will continue with division.
Step 6 :
Divide $ 270 $ by $ \color{blue}{ 84 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 7 :
Divide $ 84 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 8 :
Divide $ 18 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 9 :
Divide $ 12 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.
We can summarize an algorithm into a following table.
28458 | : | 5280 | = | 5 | remainder ( 2058 ) | ||||||||||||||||
5280 | : | 2058 | = | 2 | remainder ( 1164 ) | ||||||||||||||||
2058 | : | 1164 | = | 1 | remainder ( 894 ) | ||||||||||||||||
1164 | : | 894 | = | 1 | remainder ( 270 ) | ||||||||||||||||
894 | : | 270 | = | 3 | remainder ( 84 ) | ||||||||||||||||
270 | : | 84 | = | 3 | remainder ( 18 ) | ||||||||||||||||
84 | : | 18 | = | 4 | remainder ( 12 ) | ||||||||||||||||
18 | : | 12 | = | 1 | remainder ( 6 ) | ||||||||||||||||
12 | : | 6 | = | 2 | remainder ( 0 ) | ||||||||||||||||
GCD = 6 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.