Question

Find Greatest Common Divisor of 524 and 148, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $524$ by $148$ and get the remainder

524 : 148 = 3 ( remainder is 80)

The remainder is positive ( $80 > 0$ ), so we will continue with division.

Step 2 :
Divide $148$ by $80$ and get the remainder

148 : 80 = 1 ( remainder is 68)

The remainder is still positive ( $68 > 0$ ), so we will continue with division.

Step 3 :
Divide $80$ by $68$ and get the remainder

80 : 68 = 1 ( remainder is 12)

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

Step 4 :
Divide $68$ by $12$ and get the remainder

68 : 12 = 5 ( remainder is 8)

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

Step 5 :
Divide $12$ by $8$ and get the remainder

12 : 8 = 1 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 6 :
Divide $8$ by $4$ and get the remainder

8 : 4 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $4$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

524

148

131

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

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