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Greatest Common Divisor (GCD) of 55 and 178

The greatest common divisor (GCD) of 55 and 178 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 55 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 55 ÷ 178 = 0 remainder 55
2 178 ÷ 55 = 3 remainder 13
3 55 ÷ 13 = 4 remainder 3
4 13 ÷ 3 = 4 remainder 1
5 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
65 and 705
73 and 1201
119 and 401
188 and 724
92 and 142

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