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Greatest Common Divisor (GCD) of 125 and 37

The greatest common divisor (GCD) of 125 and 37 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 37?

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 ÷ 37 = 3 remainder 14
2 37 ÷ 14 = 2 remainder 9
3 14 ÷ 9 = 1 remainder 5
4 9 ÷ 5 = 1 remainder 4
5 5 ÷ 4 = 1 remainder 1
6 4 ÷ 1 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
25 and 1931
27 and 1191
82 and 302
105 and 987
168 and 791

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