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Greatest Common Divisor (GCD) of 139 and 170

The greatest common divisor (GCD) of 139 and 170 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 139 and 170?

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
1 139 ÷ 170 = 0 remainder 139
2 170 ÷ 139 = 1 remainder 31
3 139 ÷ 31 = 4 remainder 15
4 31 ÷ 15 = 2 remainder 1
5 15 ÷ 1 = 15 remainder 0

Examples of GCD Calculations

NumbersGCD
45 and 371
141 and 303
63 and 1391
180 and 1593
24 and 633

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