HowManyNumbers Logo

Greatest Common Divisor (GCD) of 67 and 135

The greatest common divisor (GCD) of 67 and 135 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 67 and 135?

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 67 ÷ 135 = 0 remainder 67
2 135 ÷ 67 = 2 remainder 1
3 67 ÷ 1 = 67 remainder 0

Examples of GCD Calculations

NumbersGCD
20 and 6020
16 and 1164
178 and 422
23 and 1741
173 and 591

Try Calculating GCD of Other Numbers







Related Calculators