Question

Find Greatest Common Divisor of 69 and 372, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $372$ by $69$ and get the remainder

372 : 69 = 5 ( remainder is 27)

The remainder is positive ( $27 > 0$ ), so we will continue with division.

Step 2 :
Divide $69$ by $27$ and get the remainder

69 : 27 = 2 ( remainder is 15)

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

Step 3 :
Divide $27$ by $15$ and get the remainder

27 : 15 = 1 ( remainder is 12)

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

Step 4 :
Divide $15$ by $12$ and get the remainder

15 : 12 = 1 ( remainder is 3)

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

Step 5 :
Divide $12$ by $3$ and get the remainder

12 : 3 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

372

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

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