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Greatest Common Divisor (GCD) of 59 and 84

The greatest common divisor (GCD) of 59 and 84 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 59 and 84?

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 59 ÷ 84 = 0 remainder 59
2 84 ÷ 59 = 1 remainder 25
3 59 ÷ 25 = 2 remainder 9
4 25 ÷ 9 = 2 remainder 7
5 9 ÷ 7 = 1 remainder 2
6 7 ÷ 2 = 3 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
78 and 1011
112 and 1742
145 and 321
32 and 12832
74 and 1031

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