The GCD of given numbers is 8.
Step 1 :
Divide $ 1048 $ by $ 136 $ and get the remainder
The remainder is positive ($ 96 > 0 $), so we will continue with division.
Step 2 :
Divide $ 136 $ by $ \color{blue}{ 96 } $ and get the remainder
The remainder is still positive ($ 40 > 0 $), so we will continue with division.
Step 3 :
Divide $ 96 $ by $ \color{blue}{ 40 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 4 :
Divide $ 40 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 16 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.
We can summarize an algorithm into a following table.
1048 | : | 136 | = | 7 | remainder ( 96 ) | ||||||||
136 | : | 96 | = | 1 | remainder ( 40 ) | ||||||||
96 | : | 40 | = | 2 | remainder ( 16 ) | ||||||||
40 | : | 16 | = | 2 | remainder ( 8 ) | ||||||||
16 | : | 8 | = | 2 | remainder ( 0 ) | ||||||||
GCD = 8 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.