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Greatest Common Divisor (GCD) of 125 and 192

The greatest common divisor (GCD) of 125 and 192 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 125 and 192?

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
1 125 ÷ 192 = 0 remainder 125
2 192 ÷ 125 = 1 remainder 67
3 125 ÷ 67 = 1 remainder 58
4 67 ÷ 58 = 1 remainder 9
5 58 ÷ 9 = 6 remainder 4
6 9 ÷ 4 = 2 remainder 1
7 4 ÷ 1 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
153 and 693
172 and 691
102 and 402
31 and 1321
115 and 1105

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