Question

Find Greatest Common Divisor of 49 and 620, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $620$ by $49$ and get the remainder

620 : 49 = 12 ( remainder is 32)

The remainder is positive ( $32 > 0$ ), so we will continue with division.

Step 2 :
Divide $49$ by $32$ and get the remainder

49 : 32 = 1 ( remainder is 17)

The remainder is still positive ( $17 > 0$ ), so we will continue with division.

Step 3 :
Divide $32$ by $17$ and get the remainder

32 : 17 = 1 ( remainder is 15)

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

Step 4 :
Divide $17$ by $15$ and get the remainder

17 : 15 = 1 ( remainder is 2)

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

Step 5 :
Divide $15$ by $2$ and get the remainder

15 : 2 = 7 ( remainder is 1)

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

Step 6 :
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

620

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

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