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Greatest Common Divisor (GCD) of 175 and 101

The greatest common divisor (GCD) of 175 and 101 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 101?

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 ÷ 101 = 1 remainder 74
2 101 ÷ 74 = 1 remainder 27
3 74 ÷ 27 = 2 remainder 20
4 27 ÷ 20 = 1 remainder 7
5 20 ÷ 7 = 2 remainder 6
6 7 ÷ 6 = 1 remainder 1
7 6 ÷ 1 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
144 and 153
35 and 1905
159 and 1191
84 and 1091
132 and 9933

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