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Greatest Common Divisor (GCD) of 165 and 140

The greatest common divisor (GCD) of 165 and 140 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 165 and 140?

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
1 165 ÷ 140 = 1 remainder 25
2 140 ÷ 25 = 5 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
92 and 1284
100 and 19010
72 and 291
199 and 421
185 and 411

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