Question

Find Greatest Common Divisor of 1632 and 1187, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $1632$ by $1187$ and get the remainder

1632 : 1187 = 1 ( remainder is 445)

The remainder is positive ( $445 > 0$ ), so we will continue with division.

Step 2 :
Divide $1187$ by $445$ and get the remainder

1187 : 445 = 2 ( remainder is 297)

The remainder is still positive ( $297 > 0$ ), so we will continue with division.

Step 3 :
Divide $445$ by $297$ and get the remainder

445 : 297 = 1 ( remainder is 148)

The remainder is still positive ( $148 > 0$ ), so we will continue with division.

Step 4 :
Divide $297$ by $148$ and get the remainder

297 : 148 = 2 ( remainder is 1)

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

Step 5 :
Divide $148$ by $1$ and get the remainder

148 : 1 = 148 ( 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

1632

1187

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

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