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Greatest Common Divisor (GCD) of 116 and 175

The greatest common divisor (GCD) of 116 and 175 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 175?

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 ÷ 175 = 0 remainder 116
2 175 ÷ 116 = 1 remainder 59
3 116 ÷ 59 = 1 remainder 57
4 59 ÷ 57 = 1 remainder 2
5 57 ÷ 2 = 28 remainder 1
6 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
163 and 1771
11 and 931
156 and 1511
38 and 1982
155 and 611

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