Question

Find Greatest Common Divisor of 232 and 145, using Euclidean algorithm.

Answer

The GCD of given numbers is 29.

Explanation

Step 1 :
Divide $232$ by $145$ and get the remainder

232 : 145 = 1 ( remainder is 87)

The remainder is positive ( $87 > 0$ ), so we will continue with division.

Step 2 :
Divide $145$ by $87$ and get the remainder

145 : 87 = 1 ( remainder is 58)

The remainder is still positive ( $58 > 0$ ), so we will continue with division.

Step 3 :
Divide $87$ by $58$ and get the remainder

87 : 58 = 1 ( remainder is 29)

The remainder is still positive ( $29 > 0$ ), so we will continue with division.

Step 4 :
Divide $58$ by $29$ and get the remainder

58 : 29 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $29$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

232

145

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

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