Question

Find Greatest Common Divisor of 2312 and 19520, using Euclidean algorithm.

Answer

The GCD of given numbers is 8.

Explanation

Step 1 :
Divide $19520$ by $2312$ and get the remainder

19520 : 2312 = 8 ( remainder is 1024)

The remainder is positive ( $1024 > 0$ ), so we will continue with division.

Step 2 :
Divide $2312$ by $1024$ and get the remainder

2312 : 1024 = 2 ( remainder is 264)

The remainder is still positive ( $264 > 0$ ), so we will continue with division.

Step 3 :
Divide $1024$ by $264$ and get the remainder

1024 : 264 = 3 ( remainder is 232)

The remainder is still positive ( $232 > 0$ ), so we will continue with division.

Step 4 :
Divide $264$ by $232$ and get the remainder

264 : 232 = 1 ( remainder is 32)

The remainder is still positive ( $32 > 0$ ), so we will continue with division.

Step 5 :
Divide $232$ by $32$ and get the remainder

232 : 32 = 7 ( remainder is 8)

The remainder is still positive ( $8 > 0$ ), so we will continue with division.

Step 6 :
Divide $32$ by $8$ and get the remainder

32 : 8 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $8$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

2312

19520

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

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