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Greatest Common Divisor (GCD) of 144 and 83

The greatest common divisor (GCD) of 144 and 83 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 144 and 83?

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
1 144 ÷ 83 = 1 remainder 61
2 83 ÷ 61 = 1 remainder 22
3 61 ÷ 22 = 2 remainder 17
4 22 ÷ 17 = 1 remainder 5
5 17 ÷ 5 = 3 remainder 2
6 5 ÷ 2 = 2 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
192 and 12024
121 and 491
141 and 1251
127 and 901
60 and 1191

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