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Greatest Common Divisor (GCD) of 22 and 99

The greatest common divisor (GCD) of 22 and 99 is 11.

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 22 and 99?

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 22 ÷ 99 = 0 remainder 22
2 99 ÷ 22 = 4 remainder 11
3 22 ÷ 11 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
77 and 6611
174 and 1911
23 and 811
138 and 1491
56 and 651

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