Question

Find Greatest Common Divisor of 1235 and 765, using Euclidean algorithm.

Answer

The GCD of given numbers is 5.

Explanation

Step 1 :
Divide $1235$ by $765$ and get the remainder

1235 : 765 = 1 ( remainder is 470)

The remainder is positive ( $470 > 0$ ), so we will continue with division.

Step 2 :
Divide $765$ by $470$ and get the remainder

765 : 470 = 1 ( remainder is 295)

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

Step 3 :
Divide $470$ by $295$ and get the remainder

470 : 295 = 1 ( remainder is 175)

The remainder is still positive ( $175 > 0$ ), so we will continue with division.

Step 4 :
Divide $295$ by $175$ and get the remainder

295 : 175 = 1 ( remainder is 120)

The remainder is still positive ( $120 > 0$ ), so we will continue with division.

Step 5 :
Divide $175$ by $120$ and get the remainder

175 : 120 = 1 ( remainder is 55)

The remainder is still positive ( $55 > 0$ ), so we will continue with division.

Step 6 :
Divide $120$ by $55$ and get the remainder

120 : 55 = 2 ( remainder is 10)

The remainder is still positive ( $10 > 0$ ), so we will continue with division.

Step 7 :
Divide $55$ by $10$ and get the remainder

55 : 10 = 5 ( remainder is 5)

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

Step 8 :
Divide $10$ by $5$ and get the remainder

10 : 5 = 2 ( 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

1235

765

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

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