Greatest Common Divisor (GCD) of 67 and 161
The greatest common divisor (GCD) of 67 and 161 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 67 and 161?
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 | 67 ÷ 161 = 0 remainder 67 |
| 2 | 161 ÷ 67 = 2 remainder 27 |
| 3 | 67 ÷ 27 = 2 remainder 13 |
| 4 | 27 ÷ 13 = 2 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 185 and 100 | 5 |
| 140 and 45 | 5 |
| 120 and 91 | 1 |
| 114 and 68 | 2 |
| 23 and 113 | 1 |