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Greatest Common Divisor (GCD) of 35 and 143

The greatest common divisor (GCD) of 35 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 35 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 35 ÷ 143 = 0 remainder 35
2 143 ÷ 35 = 4 remainder 3
3 35 ÷ 3 = 11 remainder 2
4 3 ÷ 2 = 1 remainder 1
5 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
69 and 243
189 and 1547
11 and 1371
55 and 761
158 and 1062

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