Question

Find Greatest Common Divisor of 63018702 and 11388300, using Euclidean algorithm.

Answer

The GCD of given numbers is 6.

Explanation

Step 1 :
Divide $63018702$ by $11388300$ and get the remainder

63018702 : 11388300 = 5 ( remainder is 6077202)

The remainder is positive ( $6077202 > 0$ ), so we will continue with division.

Step 2 :
Divide $11388300$ by $6077202$ and get the remainder

11388300 : 6077202 = 1 ( remainder is 5311098)

The remainder is still positive ( $5311098 > 0$ ), so we will continue with division.

Step 3 :
Divide $6077202$ by $5311098$ and get the remainder

6077202 : 5311098 = 1 ( remainder is 766104)

The remainder is still positive ( $766104 > 0$ ), so we will continue with division.

Step 4 :
Divide $5311098$ by $766104$ and get the remainder

5311098 : 766104 = 6 ( remainder is 714474)

The remainder is still positive ( $714474 > 0$ ), so we will continue with division.

Step 5 :
Divide $766104$ by $714474$ and get the remainder

766104 : 714474 = 1 ( remainder is 51630)

The remainder is still positive ( $51630 > 0$ ), so we will continue with division.

Step 6 :
Divide $714474$ by $51630$ and get the remainder

714474 : 51630 = 13 ( remainder is 43284)

The remainder is still positive ( $43284 > 0$ ), so we will continue with division.

Step 7 :
Divide $51630$ by $43284$ and get the remainder

51630 : 43284 = 1 ( remainder is 8346)

The remainder is still positive ( $8346 > 0$ ), so we will continue with division.

Step 8 :
Divide $43284$ by $8346$ and get the remainder

43284 : 8346 = 5 ( remainder is 1554)

The remainder is still positive ( $1554 > 0$ ), so we will continue with division.

Step 9 :
Divide $8346$ by $1554$ and get the remainder

8346 : 1554 = 5 ( remainder is 576)

The remainder is still positive ( $576 > 0$ ), so we will continue with division.

Step 10 :
Divide $1554$ by $576$ and get the remainder

1554 : 576 = 2 ( remainder is 402)

The remainder is still positive ( $402 > 0$ ), so we will continue with division.

Step 11 :
Divide $576$ by $402$ and get the remainder

576 : 402 = 1 ( remainder is 174)

The remainder is still positive ( $174 > 0$ ), so we will continue with division.

Step 12 :
Divide $402$ by $174$ and get the remainder

402 : 174 = 2 ( remainder is 54)

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

Step 13 :
Divide $174$ by $54$ and get the remainder

174 : 54 = 3 ( remainder is 12)

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

Step 14 :
Divide $54$ by $12$ and get the remainder

54 : 12 = 4 ( remainder is 6)

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

Step 15 :
Divide $12$ by $6$ and get the remainder

12 : 6 = 2 ( 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

63018702

11388300

1167013

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

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