HowManyNumbers Logo

Greatest Common Divisor (GCD) of 14 and 111

The greatest common divisor (GCD) of 14 and 111 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 14 and 111?

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 14 ÷ 111 = 0 remainder 14
2 111 ÷ 14 = 7 remainder 13
3 14 ÷ 13 = 1 remainder 1
4 13 ÷ 1 = 13 remainder 0

Examples of GCD Calculations

NumbersGCD
22 and 871
25 and 1541
60 and 1833
76 and 591
198 and 1111

Try Calculating GCD of Other Numbers







Related Calculators