Question

Find Greatest Common Divisor of 700 and 179, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $700$ by $179$ and get the remainder

700 : 179 = 3 ( remainder is 163)

The remainder is positive ( $163 > 0$ ), so we will continue with division.

Step 2 :
Divide $179$ by $163$ and get the remainder

179 : 163 = 1 ( remainder is 16)

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

Step 3 :
Divide $163$ by $16$ and get the remainder

163 : 16 = 10 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 4 :
Divide $16$ by $3$ and get the remainder

16 : 3 = 5 ( remainder is 1)

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

Step 5 :
Divide $3$ by $1$ and get the remainder

3 : 1 = 3 ( 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

700

179

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

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