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Greatest Common Divisor (GCD) of 109 and 143

The greatest common divisor (GCD) of 109 and 143 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 109 and 143?

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
1 109 ÷ 143 = 0 remainder 109
2 143 ÷ 109 = 1 remainder 34
3 109 ÷ 34 = 3 remainder 7
4 34 ÷ 7 = 4 remainder 6
5 7 ÷ 6 = 1 remainder 1
6 6 ÷ 1 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
57 and 1443
21 and 1641
94 and 1082
143 and 621
54 and 1822

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