The GCD of given numbers is 24.
Step 1 :
Divide $ 528 $ by $ 312 $ and get the remainder
The remainder is positive ($ 216 > 0 $), so we will continue with division.
Step 2 :
Divide $ 312 $ by $ \color{blue}{ 216 } $ and get the remainder
The remainder is still positive ($ 96 > 0 $), so we will continue with division.
Step 3 :
Divide $ 216 $ by $ \color{blue}{ 96 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 4 :
Divide $ 96 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 24 }} $.
We can summarize an algorithm into a following table.
528 | : | 312 | = | 1 | remainder ( 216 ) | ||||||
312 | : | 216 | = | 1 | remainder ( 96 ) | ||||||
216 | : | 96 | = | 2 | remainder ( 24 ) | ||||||
96 | : | 24 | = | 4 | remainder ( 0 ) | ||||||
GCD = 24 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.