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Greatest Common Divisor (GCD) of 25 and 165

The greatest common divisor (GCD) of 25 and 165 is 5.

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 25 and 165?

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 25 ÷ 165 = 0 remainder 25
2 165 ÷ 25 = 6 remainder 15
3 25 ÷ 15 = 1 remainder 10
4 15 ÷ 10 = 1 remainder 5
5 10 ÷ 5 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
28 and 777
160 and 171
16 and 12816
196 and 1644
161 and 1731

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