HowManyNumbers Logo

Greatest Common Divisor (GCD) of 195 and 168

The greatest common divisor (GCD) of 195 and 168 is 3.

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 195 and 168?

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
1 195 ÷ 168 = 1 remainder 27
2 168 ÷ 27 = 6 remainder 6
3 27 ÷ 6 = 4 remainder 3
4 6 ÷ 3 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
185 and 185185
99 and 153
145 and 1571
81 and 1701
92 and 1862

Try Calculating GCD of Other Numbers







Related Calculators