Question

Find Greatest Common Divisor of 1955 and 29030, using Euclidean algorithm.

Answer

The GCD of given numbers is 5.

Explanation

Step 1 :
Divide $29030$ by $1955$ and get the remainder

29030 : 1955 = 14 ( remainder is 1660)

The remainder is positive ( $1660 > 0$ ), so we will continue with division.

Step 2 :
Divide $1955$ by $1660$ and get the remainder

1955 : 1660 = 1 ( remainder is 295)

The remainder is still positive ( $295 > 0$ ), so we will continue with division.

Step 3 :
Divide $1660$ by $295$ and get the remainder

1660 : 295 = 5 ( remainder is 185)

The remainder is still positive ( $185 > 0$ ), so we will continue with division.

Step 4 :
Divide $295$ by $185$ and get the remainder

295 : 185 = 1 ( remainder is 110)

The remainder is still positive ( $110 > 0$ ), so we will continue with division.

Step 5 :
Divide $185$ by $110$ and get the remainder

185 : 110 = 1 ( remainder is 75)

The remainder is still positive ( $75 > 0$ ), so we will continue with division.

Step 6 :
Divide $110$ by $75$ and get the remainder

110 : 75 = 1 ( remainder is 35)

The remainder is still positive ( $35 > 0$ ), so we will continue with division.

Step 7 :
Divide $75$ by $35$ and get the remainder

75 : 35 = 2 ( remainder is 5)

The remainder is still positive ( $5 > 0$ ), so we will continue with division.

Step 8 :
Divide $35$ by $5$ and get the remainder

35 : 5 = 7 ( remainder is 0)

The remainder is zero => GCD is the last divisor $5$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1955

29030

2903

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

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