
Greatest Common Divisor (GCD) of 144 and 83
The greatest common divisor (GCD) of 144 and 83 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 144 and 83?
We use the Euclidean algorithm, which involves the following steps:
- Divide the larger number by the smaller number.
- Replace the larger number with the smaller number and the smaller number with the remainder from the division.
- Repeat this process until the remainder is zero.
- The non-zero remainder just before zero is the GCD.
Step-by-Step Euclidean Algorithm
Step | Calculation |
---|---|
1 | 144 ÷ 83 = 1 remainder 61 |
2 | 83 ÷ 61 = 1 remainder 22 |
3 | 61 ÷ 22 = 2 remainder 17 |
4 | 22 ÷ 17 = 1 remainder 5 |
5 | 17 ÷ 5 = 3 remainder 2 |
6 | 5 ÷ 2 = 2 remainder 1 |
7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
Numbers | GCD |
---|---|
192 and 120 | 24 |
121 and 49 | 1 |
141 and 125 | 1 |
127 and 90 | 1 |
60 and 119 | 1 |