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Greatest Common Divisor (GCD) of 111 and 68

The greatest common divisor (GCD) of 111 and 68 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 111 and 68?

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
1 111 ÷ 68 = 1 remainder 43
2 68 ÷ 43 = 1 remainder 25
3 43 ÷ 25 = 1 remainder 18
4 25 ÷ 18 = 1 remainder 7
5 18 ÷ 7 = 2 remainder 4
6 7 ÷ 4 = 1 remainder 3
7 4 ÷ 3 = 1 remainder 1
8 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
62 and 1131
80 and 1324
22 and 1602
43 and 1981
116 and 231

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