Greatest Common Divisor (GCD) of 101 and 137
The greatest common divisor (GCD) of 101 and 137 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 101 and 137?
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 | 101 ÷ 137 = 0 remainder 101 |
| 2 | 137 ÷ 101 = 1 remainder 36 |
| 3 | 101 ÷ 36 = 2 remainder 29 |
| 4 | 36 ÷ 29 = 1 remainder 7 |
| 5 | 29 ÷ 7 = 4 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 182 and 78 | 26 |
| 155 and 44 | 1 |
| 49 and 193 | 1 |
| 198 and 96 | 6 |
| 99 and 194 | 1 |