Greatest Common Divisor (GCD) of 94 and 169
The greatest common divisor (GCD) of 94 and 169 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 94 and 169?
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 | 94 ÷ 169 = 0 remainder 94 |
| 2 | 169 ÷ 94 = 1 remainder 75 |
| 3 | 94 ÷ 75 = 1 remainder 19 |
| 4 | 75 ÷ 19 = 3 remainder 18 |
| 5 | 19 ÷ 18 = 1 remainder 1 |
| 6 | 18 ÷ 1 = 18 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 165 and 105 | 15 |
| 112 and 167 | 1 |
| 106 and 191 | 1 |
| 41 and 183 | 1 |
| 49 and 58 | 1 |