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Greatest Common Divisor (GCD) of 180 and 48

The greatest common divisor (GCD) of 180 and 48 is 12.

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 180 and 48?

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
1 180 ÷ 48 = 3 remainder 36
2 48 ÷ 36 = 1 remainder 12
3 36 ÷ 12 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
61 and 1661
86 and 451
28 and 1211
31 and 1691
88 and 1911

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