Question

Find Greatest Common Divisor of 41445 and 4806, using Euclidean algorithm.

Answer

The GCD of given numbers is 27.

Explanation

Step 1 :
Divide $41445$ by $4806$ and get the remainder

41445 : 4806 = 8 ( remainder is 2997)

The remainder is positive ( $2997 > 0$ ), so we will continue with division.

Step 2 :
Divide $4806$ by $2997$ and get the remainder

4806 : 2997 = 1 ( remainder is 1809)

The remainder is still positive ( $1809 > 0$ ), so we will continue with division.

Step 3 :
Divide $2997$ by $1809$ and get the remainder

2997 : 1809 = 1 ( remainder is 1188)

The remainder is still positive ( $1188 > 0$ ), so we will continue with division.

Step 4 :
Divide $1809$ by $1188$ and get the remainder

1809 : 1188 = 1 ( remainder is 621)

The remainder is still positive ( $621 > 0$ ), so we will continue with division.

Step 5 :
Divide $1188$ by $621$ and get the remainder

1188 : 621 = 1 ( remainder is 567)

The remainder is still positive ( $567 > 0$ ), so we will continue with division.

Step 6 :
Divide $621$ by $567$ and get the remainder

621 : 567 = 1 ( remainder is 54)

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

Step 7 :
Divide $567$ by $54$ and get the remainder

567 : 54 = 10 ( remainder is 27)

The remainder is still positive ( $27 > 0$ ), so we will continue with division.

Step 8 :
Divide $54$ by $27$ and get the remainder

54 : 27 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $27$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

41445

4806

307

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

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