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Greatest Common Divisor (GCD) of 44 and 120

The greatest common divisor (GCD) of 44 and 120 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 44 and 120?

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 44 ÷ 120 = 0 remainder 44
2 120 ÷ 44 = 2 remainder 32
3 44 ÷ 32 = 1 remainder 12
4 32 ÷ 12 = 2 remainder 8
5 12 ÷ 8 = 1 remainder 4
6 8 ÷ 4 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
131 and 1401
128 and 271
83 and 501
135 and 1871
38 and 1031

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