Greatest Common Divisor (GCD) of 51 and 158
The greatest common divisor (GCD) of 51 and 158 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 51 and 158?
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 | 51 ÷ 158 = 0 remainder 51 |
| 2 | 158 ÷ 51 = 3 remainder 5 |
| 3 | 51 ÷ 5 = 10 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 174 and 73 | 1 |
| 123 and 31 | 1 |
| 189 and 43 | 1 |
| 97 and 139 | 1 |
| 115 and 140 | 5 |