Question

Find Greatest Common Divisor of 34709 and 100313, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $100313$ by $34709$ and get the remainder

100313 : 34709 = 2 ( remainder is 30895)

The remainder is positive ( $30895 > 0$ ), so we will continue with division.

Step 2 :
Divide $34709$ by $30895$ and get the remainder

34709 : 30895 = 1 ( remainder is 3814)

The remainder is still positive ( $3814 > 0$ ), so we will continue with division.

Step 3 :
Divide $30895$ by $3814$ and get the remainder

30895 : 3814 = 8 ( remainder is 383)

The remainder is still positive ( $383 > 0$ ), so we will continue with division.

Step 4 :
Divide $3814$ by $383$ and get the remainder

3814 : 383 = 9 ( remainder is 367)

The remainder is still positive ( $367 > 0$ ), so we will continue with division.

Step 5 :
Divide $383$ by $367$ and get the remainder

383 : 367 = 1 ( remainder is 16)

The remainder is still positive ( $16 > 0$ ), so we will continue with division.

Step 6 :
Divide $367$ by $16$ and get the remainder

367 : 16 = 22 ( remainder is 15)

The remainder is still positive ( $15 > 0$ ), so we will continue with division.

Step 7 :
Divide $16$ by $15$ and get the remainder

16 : 15 = 1 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 8 :
Divide $15$ by $1$ and get the remainder

15 : 1 = 15 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

34709

100313

569

100313

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

This page was created using

GCD Calculator