Question

Find Greatest Common Divisor of 104 and 64, using Euclidean algorithm.

Answer

The GCD of given numbers is 8.

Explanation

Step 1 :
Divide $104$ by $64$ and get the remainder

104 : 64 = 1 ( remainder is 40)

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

Step 2 :
Divide $64$ by $40$ and get the remainder

64 : 40 = 1 ( remainder is 24)

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

Step 3 :
Divide $40$ by $24$ and get the remainder

40 : 24 = 1 ( remainder is 16)

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

Step 4 :
Divide $24$ by $16$ and get the remainder

24 : 16 = 1 ( 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

104

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

This page was created using

GCD Calculator