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Greatest Common Divisor (GCD) of 97 and 187

The greatest common divisor (GCD) of 97 and 187 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 187?

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 ÷ 187 = 0 remainder 97
2 187 ÷ 97 = 1 remainder 90
3 97 ÷ 90 = 1 remainder 7
4 90 ÷ 7 = 12 remainder 6
5 7 ÷ 6 = 1 remainder 1
6 6 ÷ 1 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
51 and 1923
127 and 1501
152 and 284
168 and 993
60 and 213

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