Question

Find Greatest Common Divisor of 147 and 91, using Euclidean algorithm.

Answer

The GCD of given numbers is 7.

Explanation

Step 1 :
Divide $147$ by $91$ and get the remainder

147 : 91 = 1 ( remainder is 56)

The remainder is positive ( $56 > 0$ ), so we will continue with division.

Step 2 :
Divide $91$ by $56$ and get the remainder

91 : 56 = 1 ( remainder is 35)

The remainder is still positive ( $35 > 0$ ), so we will continue with division.

Step 3 :
Divide $56$ by $35$ and get the remainder

56 : 35 = 1 ( remainder is 21)

The remainder is still positive ( $21 > 0$ ), so we will continue with division.

Step 4 :
Divide $35$ by $21$ and get the remainder

35 : 21 = 1 ( remainder is 14)

The remainder is still positive ( $14 > 0$ ), so we will continue with division.

Step 5 :
Divide $21$ by $14$ and get the remainder

21 : 14 = 1 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 6 :
Divide $14$ by $7$ and get the remainder

14 : 7 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $7$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

147

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

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