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Greatest Common Divisor (GCD) of 125 and 158

The greatest common divisor (GCD) of 125 and 158 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 158?

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 ÷ 158 = 0 remainder 125
2 158 ÷ 125 = 1 remainder 33
3 125 ÷ 33 = 3 remainder 26
4 33 ÷ 26 = 1 remainder 7
5 26 ÷ 7 = 3 remainder 5
6 7 ÷ 5 = 1 remainder 2
7 5 ÷ 2 = 2 remainder 1
8 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
177 and 693
75 and 1323
176 and 1831
175 and 871
190 and 1742

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