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Greatest Common Divisor (GCD) of 111 and 45

The greatest common divisor (GCD) of 111 and 45 is 3.

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 111 and 45?

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
1 111 ÷ 45 = 2 remainder 21
2 45 ÷ 21 = 2 remainder 3
3 21 ÷ 3 = 7 remainder 0

Examples of GCD Calculations

NumbersGCD
102 and 2002
176 and 631
18 and 966
180 and 1182
44 and 1742

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