Greatest Common Divisor (GCD) of 84 and 134
The greatest common divisor (GCD) of 84 and 134 is 2.
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 84 and 134?
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 | 84 ÷ 134 = 0 remainder 84 |
| 2 | 134 ÷ 84 = 1 remainder 50 |
| 3 | 84 ÷ 50 = 1 remainder 34 |
| 4 | 50 ÷ 34 = 1 remainder 16 |
| 5 | 34 ÷ 16 = 2 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 106 and 93 | 1 |
| 53 and 115 | 1 |
| 161 and 183 | 1 |
| 76 and 167 | 1 |
| 117 and 150 | 3 |