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Greatest Common Divisor (GCD) of 97 and 133

The greatest common divisor (GCD) of 97 and 133 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 97 and 133?

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 97 ÷ 133 = 0 remainder 97
2 133 ÷ 97 = 1 remainder 36
3 97 ÷ 36 = 2 remainder 25
4 36 ÷ 25 = 1 remainder 11
5 25 ÷ 11 = 2 remainder 3
6 11 ÷ 3 = 3 remainder 2
7 3 ÷ 2 = 1 remainder 1
8 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
96 and 1582
170 and 955
133 and 7619
23 and 371
24 and 611

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