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Greatest Common Divisor (GCD) of 145 and 106

The greatest common divisor (GCD) of 145 and 106 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 145 and 106?

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
1 145 ÷ 106 = 1 remainder 39
2 106 ÷ 39 = 2 remainder 28
3 39 ÷ 28 = 1 remainder 11
4 28 ÷ 11 = 2 remainder 6
5 11 ÷ 6 = 1 remainder 5
6 6 ÷ 5 = 1 remainder 1
7 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
167 and 931
116 and 1524
79 and 851
152 and 1862
89 and 1121

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