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Greatest Common Divisor (GCD) of 125 and 17

The greatest common divisor (GCD) of 125 and 17 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 17?

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 ÷ 17 = 7 remainder 6
2 17 ÷ 6 = 2 remainder 5
3 6 ÷ 5 = 1 remainder 1
4 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
149 and 1251
143 and 1111
84 and 671
146 and 602
152 and 1048

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