Greatest Common Divisor (GCD) of 134 and 151
The greatest common divisor (GCD) of 134 and 151 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 134 and 151?
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 | 134 ÷ 151 = 0 remainder 134 |
| 2 | 151 ÷ 134 = 1 remainder 17 |
| 3 | 134 ÷ 17 = 7 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 155 and 90 | 5 |
| 123 and 136 | 1 |
| 112 and 105 | 7 |
| 137 and 14 | 1 |
| 196 and 178 | 2 |