
Greatest Common Divisor (GCD) of 180 and 121
The greatest common divisor (GCD) of 180 and 121 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 180 and 121?
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 | 180 ÷ 121 = 1 remainder 59 |
2 | 121 ÷ 59 = 2 remainder 3 |
3 | 59 ÷ 3 = 19 remainder 2 |
4 | 3 ÷ 2 = 1 remainder 1 |
5 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
Numbers | GCD |
---|---|
100 and 76 | 4 |
149 and 41 | 1 |
100 and 12 | 4 |
77 and 111 | 1 |
141 and 156 | 3 |