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Greatest Common Divisor (GCD) of 126 and 71

The greatest common divisor (GCD) of 126 and 71 is 1.

What is the Greatest Common Divisor (GCD)?

The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. It is useful in simplifying fractions, finding common factors, and in number theory.

How to Calculate the GCD of 126 and 71?

We use the Euclidean algorithm, which involves the following steps:

  1. Divide the larger number by the smaller number.
  2. Replace the larger number with the smaller number and the smaller number with the remainder from the division.
  3. Repeat this process until the remainder is zero.
  4. The non-zero remainder just before zero is the GCD.

Step-by-Step Euclidean Algorithm

StepCalculation
1 126 ÷ 71 = 1 remainder 55
2 71 ÷ 55 = 1 remainder 16
3 55 ÷ 16 = 3 remainder 7
4 16 ÷ 7 = 2 remainder 2
5 7 ÷ 2 = 3 remainder 1
6 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
163 and 1491
170 and 431
49 and 1561
45 and 341
191 and 391

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