HowManyNumbers Logo

Greatest Common Divisor (GCD) of 86 and 135

The greatest common divisor (GCD) of 86 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 86 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 86 ÷ 135 = 0 remainder 86
2 135 ÷ 86 = 1 remainder 49
3 86 ÷ 49 = 1 remainder 37
4 49 ÷ 37 = 1 remainder 12
5 37 ÷ 12 = 3 remainder 1
6 12 ÷ 1 = 12 remainder 0

Examples of GCD Calculations

NumbersGCD
61 and 771
69 and 1301
128 and 728
126 and 5418
54 and 1311

Try Calculating GCD of Other Numbers







Related Calculators