Greatest Common Divisor (GCD) of 145 and 171
The greatest common divisor (GCD) of 145 and 171 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 145 and 171?
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 | 145 ÷ 171 = 0 remainder 145 |
| 2 | 171 ÷ 145 = 1 remainder 26 |
| 3 | 145 ÷ 26 = 5 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 170 and 116 | 2 |
| 48 and 164 | 4 |
| 168 and 144 | 24 |
| 171 and 96 | 3 |
| 106 and 74 | 2 |