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Greatest Common Divisor (GCD) of 95 and 170

The greatest common divisor (GCD) of 95 and 170 is 5.

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 95 and 170?

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 95 ÷ 170 = 0 remainder 95
2 170 ÷ 95 = 1 remainder 75
3 95 ÷ 75 = 1 remainder 20
4 75 ÷ 20 = 3 remainder 15
5 20 ÷ 15 = 1 remainder 5
6 15 ÷ 5 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
55 and 531
82 and 902
31 and 451
139 and 191
192 and 342

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