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Greatest Common Divisor (GCD) of 172 and 33

The greatest common divisor (GCD) of 172 and 33 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 172 and 33?

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
1 172 ÷ 33 = 5 remainder 7
2 33 ÷ 7 = 4 remainder 5
3 7 ÷ 5 = 1 remainder 2
4 5 ÷ 2 = 2 remainder 1
5 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
166 and 571
172 and 1662
185 and 1605
133 and 721
161 and 961

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