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Greatest Common Divisor (GCD) of 147 and 82

The greatest common divisor (GCD) of 147 and 82 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 147 and 82?

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
1 147 ÷ 82 = 1 remainder 65
2 82 ÷ 65 = 1 remainder 17
3 65 ÷ 17 = 3 remainder 14
4 17 ÷ 14 = 1 remainder 3
5 14 ÷ 3 = 4 remainder 2
6 3 ÷ 2 = 1 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
134 and 1111
82 and 4141
141 and 501
49 and 1431
194 and 582

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