HowManyNumbers Logo

Greatest Common Divisor (GCD) of 110 and 178

The greatest common divisor (GCD) of 110 and 178 is 2.

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 110 and 178?

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
1 110 ÷ 178 = 0 remainder 110
2 178 ÷ 110 = 1 remainder 68
3 110 ÷ 68 = 1 remainder 42
4 68 ÷ 42 = 1 remainder 26
5 42 ÷ 26 = 1 remainder 16
6 26 ÷ 16 = 1 remainder 10
7 16 ÷ 10 = 1 remainder 6
8 10 ÷ 6 = 1 remainder 4
9 6 ÷ 4 = 1 remainder 2
10 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
65 and 1931
193 and 381
186 and 513
105 and 1323
97 and 1411

Try Calculating GCD of Other Numbers







Related Calculators