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Greatest Common Divisor (GCD) of 165 and 196

The greatest common divisor (GCD) of 165 and 196 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 165 and 196?

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 ÷ 196 = 0 remainder 165
2 196 ÷ 165 = 1 remainder 31
3 165 ÷ 31 = 5 remainder 10
4 31 ÷ 10 = 3 remainder 1
5 10 ÷ 1 = 10 remainder 0

Examples of GCD Calculations

NumbersGCD
45 and 1161
109 and 701
144 and 951
45 and 591
50 and 1311

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