Question

Find Greatest Common Divisor of 312 and 528, using Euclidean algorithm.

Answer

The GCD of given numbers is 24.

Explanation

Step 1 :
Divide $528$ by $312$ and get the remainder

528 : 312 = 1 ( remainder is 216)

The remainder is positive ( $216 > 0$ ), so we will continue with division.

Step 2 :
Divide $312$ by $216$ and get the remainder

312 : 216 = 1 ( remainder is 96)

The remainder is still positive ( $96 > 0$ ), so we will continue with division.

Step 3 :
Divide $216$ by $96$ and get the remainder

216 : 96 = 2 ( remainder is 24)

The remainder is still positive ( $24 > 0$ ), so we will continue with division.

Step 4 :
Divide $96$ by $24$ and get the remainder

96 : 24 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $24$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

312

528

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

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