Question

Find Greatest Common Divisor of 123456 and 789, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $123456$ by $789$ and get the remainder

123456 : 789 = 156 ( remainder is 372)

The remainder is positive ( $372 > 0$ ), so we will continue with division.

Step 2 :
Divide $789$ by $372$ and get the remainder

789 : 372 = 2 ( remainder is 45)

The remainder is still positive ( $45 > 0$ ), so we will continue with division.

Step 3 :
Divide $372$ by $45$ and get the remainder

372 : 45 = 8 ( remainder is 12)

The remainder is still positive ( $12 > 0$ ), so we will continue with division.

Step 4 :
Divide $45$ by $12$ and get the remainder

45 : 12 = 3 ( remainder is 9)

The remainder is still positive ( $9 > 0$ ), so we will continue with division.

Step 5 :
Divide $12$ by $9$ and get the remainder

12 : 9 = 1 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 6 :
Divide $9$ by $3$ and get the remainder

9 : 3 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

123456

789

643

263

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

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