HowManyNumbers Logo

Greatest Common Divisor (GCD) of 116 and 187

The greatest common divisor (GCD) of 116 and 187 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 116 and 187?

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
1 116 ÷ 187 = 0 remainder 116
2 187 ÷ 116 = 1 remainder 71
3 116 ÷ 71 = 1 remainder 45
4 71 ÷ 45 = 1 remainder 26
5 45 ÷ 26 = 1 remainder 19
6 26 ÷ 19 = 1 remainder 7
7 19 ÷ 7 = 2 remainder 5
8 7 ÷ 5 = 1 remainder 2
9 5 ÷ 2 = 2 remainder 1
10 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
158 and 371
169 and 491
114 and 651
13 and 661
61 and 1671

Try Calculating GCD of Other Numbers







Related Calculators