HowManyNumbers Logo

Greatest Common Divisor (GCD) of 75 and 192

The greatest common divisor (GCD) of 75 and 192 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 75 and 192?

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 75 ÷ 192 = 0 remainder 75
2 192 ÷ 75 = 2 remainder 42
3 75 ÷ 42 = 1 remainder 33
4 42 ÷ 33 = 1 remainder 9
5 33 ÷ 9 = 3 remainder 6
6 9 ÷ 6 = 1 remainder 3
7 6 ÷ 3 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
147 and 8421
99 and 819
21 and 1941
45 and 555
30 and 726

Try Calculating GCD of Other Numbers







Related Calculators