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Greatest Common Divisor (GCD) of 73 and 111

The greatest common divisor (GCD) of 73 and 111 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 73 and 111?

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 73 ÷ 111 = 0 remainder 73
2 111 ÷ 73 = 1 remainder 38
3 73 ÷ 38 = 1 remainder 35
4 38 ÷ 35 = 1 remainder 3
5 35 ÷ 3 = 11 remainder 2
6 3 ÷ 2 = 1 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
102 and 322
171 and 851
200 and 1244
133 and 1571
70 and 17010

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