HowManyNumbers Logo

Greatest Common Divisor (GCD) of 120 and 50

The greatest common divisor (GCD) of 120 and 50 is 10.

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 120 and 50?

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
1 120 ÷ 50 = 2 remainder 20
2 50 ÷ 20 = 2 remainder 10
3 20 ÷ 10 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
34 and 1602
62 and 111
179 and 1531
112 and 1057
15 and 843

Try Calculating GCD of Other Numbers







Related Calculators