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Greatest Common Divisor (GCD) of 91 and 45

The greatest common divisor (GCD) of 91 and 45 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 91 and 45?

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 91 ÷ 45 = 2 remainder 1
2 45 ÷ 1 = 45 remainder 0

Examples of GCD Calculations

NumbersGCD
169 and 1911
119 and 1411
160 and 111
94 and 1851
98 and 1691

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