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Greatest Common Divisor (GCD) of 60 and 107

The greatest common divisor (GCD) of 60 and 107 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 60 and 107?

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 60 ÷ 107 = 0 remainder 60
2 107 ÷ 60 = 1 remainder 47
3 60 ÷ 47 = 1 remainder 13
4 47 ÷ 13 = 3 remainder 8
5 13 ÷ 8 = 1 remainder 5
6 8 ÷ 5 = 1 remainder 3
7 5 ÷ 3 = 1 remainder 2
8 3 ÷ 2 = 1 remainder 1
9 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
122 and 1891
101 and 1621
194 and 302
155 and 605
80 and 1155

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