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Greatest Common Divisor (GCD) of 124 and 195

The greatest common divisor (GCD) of 124 and 195 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 124 and 195?

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
1 124 ÷ 195 = 0 remainder 124
2 195 ÷ 124 = 1 remainder 71
3 124 ÷ 71 = 1 remainder 53
4 71 ÷ 53 = 1 remainder 18
5 53 ÷ 18 = 2 remainder 17
6 18 ÷ 17 = 1 remainder 1
7 17 ÷ 1 = 17 remainder 0

Examples of GCD Calculations

NumbersGCD
175 and 1721
64 and 1884
137 and 1941
163 and 841
139 and 101

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