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Greatest Common Divisor (GCD) of 169 and 75

The greatest common divisor (GCD) of 169 and 75 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 169 and 75?

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
1 169 ÷ 75 = 2 remainder 19
2 75 ÷ 19 = 3 remainder 18
3 19 ÷ 18 = 1 remainder 1
4 18 ÷ 1 = 18 remainder 0

Examples of GCD Calculations

NumbersGCD
14 and 8414
148 and 622
41 and 4141
182 and 971
22 and 491

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