The GCD of given numbers is 16.
Step 1 :
Divide $ 960 $ by $ 112 $ and get the remainder
The remainder is positive ($ 64 > 0 $), so we will continue with division.
Step 2 :
Divide $ 112 $ by $ \color{blue}{ 64 } $ and get the remainder
The remainder is still positive ($ 48 > 0 $), so we will continue with division.
Step 3 :
Divide $ 64 $ by $ \color{blue}{ 48 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 4 :
Divide $ 48 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 16 }} $.
We can summarize an algorithm into a following table.
960 | : | 112 | = | 8 | remainder ( 64 ) | ||||||
112 | : | 64 | = | 1 | remainder ( 48 ) | ||||||
64 | : | 48 | = | 1 | remainder ( 16 ) | ||||||
48 | : | 16 | = | 3 | remainder ( 0 ) | ||||||
GCD = 16 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.