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Greatest Common Divisor (GCD) of 175 and 181

The greatest common divisor (GCD) of 175 and 181 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 175 and 181?

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
1 175 ÷ 181 = 0 remainder 175
2 181 ÷ 175 = 1 remainder 6
3 175 ÷ 6 = 29 remainder 1
4 6 ÷ 1 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
81 and 851
24 and 1026
146 and 702
173 and 1601
58 and 1211

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