HowManyNumbers Logo

Greatest Common Divisor (GCD) of 105 and 145

The greatest common divisor (GCD) of 105 and 145 is 5.

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 105 and 145?

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
1 105 ÷ 145 = 0 remainder 105
2 145 ÷ 105 = 1 remainder 40
3 105 ÷ 40 = 2 remainder 25
4 40 ÷ 25 = 1 remainder 15
5 25 ÷ 15 = 1 remainder 10
6 15 ÷ 10 = 1 remainder 5
7 10 ÷ 5 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
26 and 1582
185 and 631
120 and 462
20 and 1091
158 and 931

Try Calculating GCD of Other Numbers







Related Calculators