Greatest Common Divisor (GCD) of 91 and 145
The greatest common divisor (GCD) of 91 and 145 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 91 and 145?
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 | 91 ÷ 145 = 0 remainder 91 |
| 2 | 145 ÷ 91 = 1 remainder 54 |
| 3 | 91 ÷ 54 = 1 remainder 37 |
| 4 | 54 ÷ 37 = 1 remainder 17 |
| 5 | 37 ÷ 17 = 2 remainder 3 |
| 6 | 17 ÷ 3 = 5 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 163 and 95 | 1 |
| 62 and 146 | 2 |
| 89 and 67 | 1 |
| 199 and 115 | 1 |
| 11 and 190 | 1 |