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Greatest Common Divisor (GCD) of 124 and 132

The greatest common divisor (GCD) of 124 and 132 is 4.

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 124 and 132?

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
1 124 ÷ 132 = 0 remainder 124
2 132 ÷ 124 = 1 remainder 8
3 124 ÷ 8 = 15 remainder 4
4 8 ÷ 4 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
94 and 882
50 and 611
97 and 1171
45 and 333
34 and 1802

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