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Greatest Common Divisor (GCD) of 28 and 72

The greatest common divisor (GCD) of 28 and 72 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 28 and 72?

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 28 ÷ 72 = 0 remainder 28
2 72 ÷ 28 = 2 remainder 16
3 28 ÷ 16 = 1 remainder 12
4 16 ÷ 12 = 1 remainder 4
5 12 ÷ 4 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
78 and 1413
137 and 1501
64 and 1404
30 and 1131
14 and 1511

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