Greatest Common Divisor (GCD) of 117 and 169
The greatest common divisor (GCD) of 117 and 169 is 13.
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 117 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 | 117 ÷ 169 = 0 remainder 117 |
| 2 | 169 ÷ 117 = 1 remainder 52 |
| 3 | 117 ÷ 52 = 2 remainder 13 |
| 4 | 52 ÷ 13 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 181 and 192 | 1 |
| 170 and 166 | 2 |
| 51 and 187 | 17 |
| 60 and 69 | 3 |
| 134 and 62 | 2 |