Question

Find Greatest Common Divisor of 44838 and 4830, using Euclidean algorithm.

Answer

The GCD of given numbers is 6.

Explanation

Step 1 :
Divide $44838$ by $4830$ and get the remainder

44838 : 4830 = 9 ( remainder is 1368)

The remainder is positive ( $1368 > 0$ ), so we will continue with division.

Step 2 :
Divide $4830$ by $1368$ and get the remainder

4830 : 1368 = 3 ( remainder is 726)

The remainder is still positive ( $726 > 0$ ), so we will continue with division.

Step 3 :
Divide $1368$ by $726$ and get the remainder

1368 : 726 = 1 ( remainder is 642)

The remainder is still positive ( $642 > 0$ ), so we will continue with division.

Step 4 :
Divide $726$ by $642$ and get the remainder

726 : 642 = 1 ( remainder is 84)

The remainder is still positive ( $84 > 0$ ), so we will continue with division.

Step 5 :
Divide $642$ by $84$ and get the remainder

642 : 84 = 7 ( remainder is 54)

The remainder is still positive ( $54 > 0$ ), so we will continue with division.

Step 6 :
Divide $84$ by $54$ and get the remainder

84 : 54 = 1 ( remainder is 30)

The remainder is still positive ( $30 > 0$ ), so we will continue with division.

Step 7 :
Divide $54$ by $30$ and get the remainder

54 : 30 = 1 ( remainder is 24)

The remainder is still positive ( $24 > 0$ ), so we will continue with division.

Step 8 :
Divide $30$ by $24$ and get the remainder

30 : 24 = 1 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 9 :
Divide $24$ by $6$ and get the remainder

24 : 6 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $6$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

44838

4830

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

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