HowManyNumbers Logo

Greatest Common Divisor (GCD) of 114 and 72

The greatest common divisor (GCD) of 114 and 72 is 6.

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 114 and 72?

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
1 114 ÷ 72 = 1 remainder 42
2 72 ÷ 42 = 1 remainder 30
3 42 ÷ 30 = 1 remainder 12
4 30 ÷ 12 = 2 remainder 6
5 12 ÷ 6 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
139 and 1351
37 and 171
33 and 1143
87 and 1671
65 and 891

Try Calculating GCD of Other Numbers







Related Calculators