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Greatest Common Divisor (GCD) of 84 and 101

The greatest common divisor (GCD) of 84 and 101 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 84 and 101?

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 84 ÷ 101 = 0 remainder 84
2 101 ÷ 84 = 1 remainder 17
3 84 ÷ 17 = 4 remainder 16
4 17 ÷ 16 = 1 remainder 1
5 16 ÷ 1 = 16 remainder 0

Examples of GCD Calculations

NumbersGCD
181 and 1351
72 and 851
58 and 151
183 and 1743
21 and 851

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