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Greatest Common Divisor (GCD) of 143 and 58

The greatest common divisor (GCD) of 143 and 58 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 143 and 58?

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
1 143 ÷ 58 = 2 remainder 27
2 58 ÷ 27 = 2 remainder 4
3 27 ÷ 4 = 6 remainder 3
4 4 ÷ 3 = 1 remainder 1
5 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
56 and 1711
168 and 1391
44 and 1191
21 and 1671
166 and 1091

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