Greatest Common Divisor (GCD) of 132 and 169
The greatest common divisor (GCD) of 132 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 132 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 | 132 ÷ 169 = 0 remainder 132 |
| 2 | 169 ÷ 132 = 1 remainder 37 |
| 3 | 132 ÷ 37 = 3 remainder 21 |
| 4 | 37 ÷ 21 = 1 remainder 16 |
| 5 | 21 ÷ 16 = 1 remainder 5 |
| 6 | 16 ÷ 5 = 3 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 191 and 115 | 1 |
| 193 and 25 | 1 |
| 196 and 113 | 1 |
| 131 and 105 | 1 |
| 73 and 94 | 1 |