The GCD of given numbers is 2.
Step 1 :
Divide $ 8496 $ by $ 5234 $ and get the remainder
The remainder is positive ($ 3262 > 0 $), so we will continue with division.
Step 2 :
Divide $ 5234 $ by $ \color{blue}{ 3262 } $ and get the remainder
The remainder is still positive ($ 1972 > 0 $), so we will continue with division.
Step 3 :
Divide $ 3262 $ by $ \color{blue}{ 1972 } $ and get the remainder
The remainder is still positive ($ 1290 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1972 $ by $ \color{blue}{ 1290 } $ and get the remainder
The remainder is still positive ($ 682 > 0 $), so we will continue with division.
Step 5 :
Divide $ 1290 $ by $ \color{blue}{ 682 } $ and get the remainder
The remainder is still positive ($ 608 > 0 $), so we will continue with division.
Step 6 :
Divide $ 682 $ by $ \color{blue}{ 608 } $ and get the remainder
The remainder is still positive ($ 74 > 0 $), so we will continue with division.
Step 7 :
Divide $ 608 $ by $ \color{blue}{ 74 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 8 :
Divide $ 74 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 9 :
Divide $ 16 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 10 :
Divide $ 10 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 11 :
Divide $ 6 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 12 :
Divide $ 4 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
8496 | : | 5234 | = | 1 | remainder ( 3262 ) | ||||||||||||||||||||||
5234 | : | 3262 | = | 1 | remainder ( 1972 ) | ||||||||||||||||||||||
3262 | : | 1972 | = | 1 | remainder ( 1290 ) | ||||||||||||||||||||||
1972 | : | 1290 | = | 1 | remainder ( 682 ) | ||||||||||||||||||||||
1290 | : | 682 | = | 1 | remainder ( 608 ) | ||||||||||||||||||||||
682 | : | 608 | = | 1 | remainder ( 74 ) | ||||||||||||||||||||||
608 | : | 74 | = | 8 | remainder ( 16 ) | ||||||||||||||||||||||
74 | : | 16 | = | 4 | remainder ( 10 ) | ||||||||||||||||||||||
16 | : | 10 | = | 1 | remainder ( 6 ) | ||||||||||||||||||||||
10 | : | 6 | = | 1 | remainder ( 4 ) | ||||||||||||||||||||||
6 | : | 4 | = | 1 | remainder ( 2 ) | ||||||||||||||||||||||
4 | : | 2 | = | 2 | remainder ( 0 ) | ||||||||||||||||||||||
GCD = 2 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.