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Greatest Common Divisor (GCD) of 53 and 51

The greatest common divisor (GCD) of 53 and 51 is 1.

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 53 and 51?

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 53 ÷ 51 = 1 remainder 2
2 51 ÷ 2 = 25 remainder 1
3 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
38 and 1542
75 and 891
123 and 1053
23 and 581
60 and 1593

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