Question

Find Greatest Common Divisor of 91261 and 117035, using Euclidean algorithm.

Answer

The GCD of given numbers is 263.

Explanation

Step 1 :
Divide $117035$ by $91261$ and get the remainder

117035 : 91261 = 1 ( remainder is 25774)

The remainder is positive ( $25774 > 0$ ), so we will continue with division.

Step 2 :
Divide $91261$ by $25774$ and get the remainder

91261 : 25774 = 3 ( remainder is 13939)

The remainder is still positive ( $13939 > 0$ ), so we will continue with division.

Step 3 :
Divide $25774$ by $13939$ and get the remainder

25774 : 13939 = 1 ( remainder is 11835)

The remainder is still positive ( $11835 > 0$ ), so we will continue with division.

Step 4 :
Divide $13939$ by $11835$ and get the remainder

13939 : 11835 = 1 ( remainder is 2104)

The remainder is still positive ( $2104 > 0$ ), so we will continue with division.

Step 5 :
Divide $11835$ by $2104$ and get the remainder

11835 : 2104 = 5 ( remainder is 1315)

The remainder is still positive ( $1315 > 0$ ), so we will continue with division.

Step 6 :
Divide $2104$ by $1315$ and get the remainder

2104 : 1315 = 1 ( remainder is 789)

The remainder is still positive ( $789 > 0$ ), so we will continue with division.

Step 7 :
Divide $1315$ by $789$ and get the remainder

1315 : 789 = 1 ( remainder is 526)

The remainder is still positive ( $526 > 0$ ), so we will continue with division.

Step 8 :
Divide $789$ by $526$ and get the remainder

789 : 526 = 1 ( remainder is 263)

The remainder is still positive ( $263 > 0$ ), so we will continue with division.

Step 9 :
Divide $526$ by $263$ and get the remainder

526 : 263 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $263$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

91261

117035

263

347

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

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