HowManyNumbers Logo

Greatest Common Divisor (GCD) of 143 and 89

The greatest common divisor (GCD) of 143 and 89 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 143 and 89?

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
1 143 ÷ 89 = 1 remainder 54
2 89 ÷ 54 = 1 remainder 35
3 54 ÷ 35 = 1 remainder 19
4 35 ÷ 19 = 1 remainder 16
5 19 ÷ 16 = 1 remainder 3
6 16 ÷ 3 = 5 remainder 1
7 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
185 and 571
162 and 1113
187 and 781
62 and 362
167 and 951

Try Calculating GCD of Other Numbers







Related Calculators