Greatest Common Divisor (GCD) of 101 and 58
The greatest common divisor (GCD) of 101 and 58 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 58?
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 ÷ 58 = 1 remainder 43 |
| 2 | 58 ÷ 43 = 1 remainder 15 |
| 3 | 43 ÷ 15 = 2 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 175 and 197 | 1 |
| 19 and 97 | 1 |
| 105 and 150 | 15 |
| 147 and 72 | 3 |
| 10 and 93 | 1 |