Question

Find Greatest Common Divisor of 5504 and 385, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $5504$ by $385$ and get the remainder

5504 : 385 = 14 ( remainder is 114)

The remainder is positive ( $114 > 0$ ), so we will continue with division.

Step 2 :
Divide $385$ by $114$ and get the remainder

385 : 114 = 3 ( remainder is 43)

The remainder is still positive ( $43 > 0$ ), so we will continue with division.

Step 3 :
Divide $114$ by $43$ and get the remainder

114 : 43 = 2 ( remainder is 28)

The remainder is still positive ( $28 > 0$ ), so we will continue with division.

Step 4 :
Divide $43$ by $28$ and get the remainder

43 : 28 = 1 ( remainder is 15)

The remainder is still positive ( $15 > 0$ ), so we will continue with division.

Step 5 :
Divide $28$ by $15$ and get the remainder

28 : 15 = 1 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 6 :
Divide $15$ by $13$ and get the remainder

15 : 13 = 1 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 7 :
Divide $13$ by $2$ and get the remainder

13 : 2 = 6 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 8 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

5504

385

The GCD equals the product of the numbers at the intersection.

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