Greatest Common Divisor (GCD) of 137 and 80
The greatest common divisor (GCD) of 137 and 80 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 137 and 80?
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 | 137 ÷ 80 = 1 remainder 57 |
| 2 | 80 ÷ 57 = 1 remainder 23 |
| 3 | 57 ÷ 23 = 2 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 15 and 36 | 3 |
| 121 and 157 | 1 |
| 84 and 145 | 1 |
| 152 and 85 | 1 |
| 190 and 77 | 1 |