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Greatest Common Divisor (GCD) of 175 and 38

The greatest common divisor (GCD) of 175 and 38 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 175 and 38?

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
1 175 ÷ 38 = 4 remainder 23
2 38 ÷ 23 = 1 remainder 15
3 23 ÷ 15 = 1 remainder 8
4 15 ÷ 8 = 1 remainder 7
5 8 ÷ 7 = 1 remainder 1
6 7 ÷ 1 = 7 remainder 0

Examples of GCD Calculations

NumbersGCD
149 and 341
26 and 1122
76 and 1244
191 and 841
142 and 1471

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