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Greatest Common Divisor (GCD) of 133 and 51

The greatest common divisor (GCD) of 133 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 133 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
1 133 ÷ 51 = 2 remainder 31
2 51 ÷ 31 = 1 remainder 20
3 31 ÷ 20 = 1 remainder 11
4 20 ÷ 11 = 1 remainder 9
5 11 ÷ 9 = 1 remainder 2
6 9 ÷ 2 = 4 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
93 and 723
44 and 311
120 and 16515
98 and 1871
119 and 1601

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