Question

Find Greatest Common Divisor of 1048 and 136, using Euclidean algorithm.

Answer

The GCD of given numbers is 8.

Explanation

Step 1 :
Divide $1048$ by $136$ and get the remainder

1048 : 136 = 7 ( remainder is 96)

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

Step 2 :
Divide $136$ by $96$ and get the remainder

136 : 96 = 1 ( remainder is 40)

The remainder is still positive ( $40 > 0$ ), so we will continue with division.

Step 3 :
Divide $96$ by $40$ and get the remainder

96 : 40 = 2 ( remainder is 16)

The remainder is still positive ( $16 > 0$ ), so we will continue with division.

Step 4 :
Divide $40$ by $16$ and get the remainder

40 : 16 = 2 ( remainder is 8)

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

Step 5 :
Divide $16$ by $8$ and get the remainder

16 : 8 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $8$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1048

136

131

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

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