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Greatest Common Divisor (GCD) of 97 and 126

The greatest common divisor (GCD) of 97 and 126 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 97 and 126?

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 97 ÷ 126 = 0 remainder 97
2 126 ÷ 97 = 1 remainder 29
3 97 ÷ 29 = 3 remainder 10
4 29 ÷ 10 = 2 remainder 9
5 10 ÷ 9 = 1 remainder 1
6 9 ÷ 1 = 9 remainder 0

Examples of GCD Calculations

NumbersGCD
148 and 1911
69 and 1371
176 and 1531
134 and 462
114 and 1506

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